I have 18 statistic proplems

1. Hallux abducto valgus (call it HAV) is a deformation of the big toe that often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 38 consecutive patients under the age of 21 who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. Here are the data.

It is reasonable to regard these patients as a random sample of young patients who require HAV surgery. Given a 95% confidence interval for the mean HAV angle in the population of all such patients, find the following.

Confidence Interval:
 ° to  ° 
Conclusion

The mean HAV angle among such patients will always be within this interval 95% of the time.We are 95% confident that the mean HAV angle among such patients is outside this interval.    The mean HAV angle among such patients will always be outside this interval 95% of the time.We are 95% confident that the mean HAV angle among such patients is within this interval.

1. Subjects with pre-existing cardiovascular symptoms who were receiving subitramine, an appetite suppressant, were found to be at increased risk of cardiovascular events while taking the drug. The study included 9804 overweight or obese subjects with pre-existing cardiovascular disease and/or type 2 diabetes. The subjects were randomly assigned to subitramine (4906 subjects) or a placebo (4898 subjects) in a double-blind fashion. The primary outcome measured was the occurrence of any of the following events: nonfatal myocardial infarction or stroke, resuscitation after cardiac arrest, or cardiovascular death. The primary outcome was observed in 565 subjects in the subitramine group and 492 subjects in the placebo group. 
   Does the data give good reason to think that there is a difference between the proportions of treatment and placebo subjects who experienced the primary outcome? 
   State the hypotheses. Find the test statistic and the P-value. (Round test statistic to two decimal places and P-value to four decimal places.)

State your conclusion. (Use α = 0.05.)

Because the P-value is large, we have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.Because the P-value is large, we do not have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.    Because the P-value is small, we do not have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.Because the P-value is small, we have evidence that there is a difference in the proportion of "primary outcomes" between subitramine and placebo.

3. A random sample of 49 measurements from one population had a sample mean of 12, with sample standard deviation 5. An independent random sample of 64 measurements from a second population had a sample mean of 15, with sample standard deviation 6. Test the claim that the population means are different. Use level of significance 0.01.

(a) What distribution does the sample test statistic follow? 

The Student's t. We assume that both population distributions are approximately normal with unknown population standard deviations.The standard normal. We assume that both population distributions are approximately normal with known population standard deviations.    The standard normal. We assume that both population distributions are approximately normal with unknown population standard deviations.The Student's t. We assume that both population distributions are approximately normal with known population standard deviations.

(b) State the hypotheses.

H0: μ1 = μ2; H1: μ1 ≠ μ2H0: μ1 ≠ μ2; H1: μ1 = μ2    H0: μ1 = μ2; H1: μ1 < μ2H0: μ1 = μ2; H1: μ1 > μ2

(c) Estimate the P-value of the sample test statistic.

P-value > 0.5000.250 < P-value < 0.500    0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

(d) Conclude the test.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret the results.

Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.     Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.

4.Question DetailsMy Notes

In a study of exhaust emissions from school buses, the pollution intake by passengers was determined for a sample of nine school buses used in the Southern California Air Basin. The pollution intake is the amount of exhaust emissions, in grams per person, that would be inhaled while traveling on the bus during its usual 18-mile trip on congested freeways from South Central LA to a magnet school in West LA. Here are the amounts for the nine buses when driven with the windows open.

1.11     0.33    0.40     0.33     1.35     0.38     0.25     0.40     0.35

(a) Consider making a stemplot. Are there outliers or strong skewness that would preclude use of the t procedures?

The distribution is symmetric so use of t procedures is appropriate.The distribution has a slight right skew, but no potential outliers, so the use of t procedures is still appropriate.    The sample is small and the stemplot is left skewed with possible outliers, so use of t procedures is not appropriate.The sample is small and the stemplot is right skewed with possible outliers, so use of t procedures is not appropriate.

(b) A good way to judge the effect of outliers is to do your analysis twice, once with the outliers and a second time without them. Give a 90% confidence interval, with all the data, for the mean pollution intake among all school buses used in the Southern California Air Basin that travel the route investigated in the study. 
 to  
Give a 90% confidence interval with the outliers removed.
 to  
(c) Compare the two intervals in part (b). What is the most important effect of removing the outliers?

Without the outliers, there is a smaller margin of error.Without the outliers, there is a larger margin of error.    

5.Question DetailsMy Notes

How strong a force (in pounds) is needed to pull apart pieces of wood 4 inches long and 1.5 inches square? The following are data from students performing a comparable laboratory exercise. Suppose that the strength of pieces of wood like these follow a Normal distribution with standard deviation 3000 pounds.

(a) We are interested in statistical significant evidence at the 

α = 0.10

 level for a claim that the mean is 32,500 pounds. 
What are the null and alternative hypotheses? 

H0: μ = 32,500
H1: μ < 32,500H0: μ = 32,500
H1: μ > 32,500    H0: μ = 32,500
H1: μ ≠ 32,500H0: μ ≠ 32,500
H1: μ = 32,500

What is the value of the test statistic. (Round your answer to two decimal places.) 
z =  
What is the P-value of the test? (Round your answer to four decimal places.) 
P-value =  
What is your conclusion? 

There is enough evidence to conclude that the wood's mean strength differs from 32,500 pounds.There is not enough evidence to conclude that the wood's mean strength differs from 32,500 pounds.    

(b) We are interested in statistical significant evidence at the 

α = 0.10

 level for a claim that the mean is 31,500 pounds. 
What are the null and alternative hypotheses? 

H0: μ = 31,500
H1: μ > 31,500H0: μ ≠ 31,500
Ha: μ = 31,500    H0: μ = 31,500
H1: μ ≠ 31,500H0: μ = 31,500
H1: μ < 31,500

What is the value of the test statistic. (Round your answer to two decimal places.) 
z =  
What is the P-value of the test? (Round your answer to four decimal places.) 
P-value =  
What is your conclusion? 

There is enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.There is not enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.    

6.Question Details |  Previous AnswersMy Notes

A sample mean of x = 2.15 was obtained from a random sample of 49 items, with a sample standard deviation of 0.72. Do the sample data indicate that the population mean is more than 1.90? Use α = 0.05.

(a) Identify the claim, the null hypothesis, and the alternative hypothesis.

(b) Will you use a left-tailed, right-tailed, or two-tailed test?

right-tailedleft-tailed    two-tailed

(c) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is unknown.The Student's t, since the sample size is large and σ is unknown.    The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known.The Student's t, since we assume that x has a normal distribution and σ is known.The Student's t, since we assume that x has a normal distribution and σ is unknown.

(d) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(e) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(f) State your conclusion.

Fail to reject the null hypothesis, there is insufficient evidence that the population mean is more than 1.90.Fail to reject the null hypothesis, there is sufficient evidence that the population mean is more than 1.90.    Reject the null hypothesis, there is insufficient evidence that the population mean is more than 1.90.Reject the null hypothesis, there is sufficient evidence that the population mean is more than 1.90.

7.Question DetailsMy Notes

Arsenic occurs naturally in some ground water. A mean arsenic level of 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This particular well is tested on a regular basis for arsenic. A random sample of 31 tests gave a sample mean of x = 7.0 ppb arsenic, with sample standard deviation of 2.2 ppb. Does this information indicate that the average level of arsenic in this well is less than 8 ppb? Use α = 0.05.

(a) Identify the claim, the null hypothesis, and the alternative hypothesis.

(b) Will you use a left-tailed, right-tailed, or two-tailed test?

right-tailedtwo-tailed    left-tailed

(c) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is unknown.The Student's t, since we assume that x has a normal distribution and σ is known.    The Student's t, since the sample size is large and σ is unknown.The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known.The Student's t, since we assume that x has a normal distribution and σ is unknown.

(d) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(e) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(f) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence that the average arsenic content is less than 8 ppb.Fail to reject the null hypothesis, there is sufficient evidence that the average arsenic content is less than 8 ppb.    Reject the null hypothesis, there is insufficient evidence that the average arsenic content is less than 8 ppb.Reject the null hypothesis, there is sufficient evidence that the average arsenic content is less than 8 ppb.

8.Question DetailsMy Notes

A random sample of 49 adult coyotes in a region of Minnesota showed the average age to be x = 1.97 years, with sample standard deviation of 0.82 years. However, it is thought that the overall population mean age of coyotes is approximately 1.75. Does the data indicate that coyotes in the sampled region of Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01.

(a) Identify the claim, the null hypothesis, and the alternative hypothesis.

(b) Will you use a left-tailed, right-tailed, or two-tailed test?

right-tailedleft-tailed    two-tailed

(c) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since we assume that x has a normal distribution and σ is unknown.The standard normal, since the sample size is large and σ is unknown.    The Student's t, since we assume that x has a normal distribution and σ is known.The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is unknown.

(d) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(e) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(f) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence that the average age of Minnesota coyotes is greater than 1.75 years.Fail to reject the null hypothesis, there is sufficient evidence that the average age of Minnesota coyotes is greater than 1.75 years.    Reject the null hypothesis, there is insufficient evidence that the average age of Minnesota coyotes is greater than 1.75 years.Reject the null hypothesis, there is sufficient evidence that the average age of Minnesota coyotes is greater than 1.75 years.

9.Question DetailsMy Notes

A professional employee in a large corporation has typically received an average of 41.7 e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 41 employees showed that they were receiving an average of x = 37.0 e-mails per day. The computer server through which e-mails are routed has shown that σ = 18.2. Has the new policy had any effect? Use a 10% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee.

(a) Identify the claim, the null hypothesis, and the alternative hypothesis.

(b) Will you use a left-tailed, right-tailed, or two-tailed test?

right-tailedleft-tailed    two-tailed

(c) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we know that x has a normal distribution with known σ.The standard normal, since the sample size is large and σ is unknown.    The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known.The standard normal, since we know that x has a normal distribution with unknown σ.The Student's t, since the sample size is large and σ is unknown.

(d) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(e) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.    At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(f) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the average number of e-mails differs under the new priority system.Reject the null hypothesis, there is insufficient evidence that the average number of e-mails differs under the new priority system.    Reject the null hypothesis, there is sufficient evidence that the average number of e-mails differs under the new priority system.Fail to reject the null hypothesis, there is insufficient evidence that the average number of e-mails differs under the new priority system.

10.Question DetailsMy Notes

Let x be a random variable that represents assembly times for the Ford Taurus. A research journal reported that the typical assembly time had been 38 hours. A modification to the assembly procedure has been made. Experience with assembly methods indicates that σ = 1.0 hours. It is thought that the average assembly time may be reduced by this new modification. A random sample of 47 new Ford Taurus automobiles coming off the assembly line showed the average assembly time using the new method to be x = 37.50 hours. Does the data support the claim that the average assembly time has now been reduced? Use α = 0.10.

(a) Identify the claim, the null hypothesis, and the alternative hypothesis.

(b) Will you use a left-tailed, right-tailed, or two-tailed test?

right-tailedtwo-tailed    left-tailed

(c) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is unknown.The standard normal, since we know that x has a normal distribution with known σ.    The Student's t, since the sample size is large and σ is unknown.The standard normal, since we know that x has a normal distribution with unknown σ.The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known.

(d) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(e) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(f) State your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the average assembly time is less than 38 hours.Fail to reject the null hypothesis, there is insufficient evidence that the average assembly time is less than 38 hours.    Fail to reject the null hypothesis, there is sufficient evidence that the average assembly time is less than 38 hours.Reject the null hypothesis, there is insufficient evidence that the average assembly time is less than 38 hours.

11.Question DetailsMy Notes

Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).

Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that σ = 15.2. An average glucose level for horses is 86 (mg/100 ml). Do these sample data values indicate that Gentle Ben has a mean glucose level higher than 86? Use α = 0.01.

(a) Enter the following.
x =  
s =  
(b) Identify the claim, the null hypothesis, and the alternative hypothesis.

(c) Will you use a left-tailed, right-tailed, or two-tailed test?

two-tailedleft-tailed    right-tailed

(d) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since n is large with known σ.The Student's t, since we assume that x has a normal distribution with known σ.    The standard normal, since we assume that x has a normal distribution with unknown σ.The standard normal, since we assume that x has a normal distribution with known σ.The standard normal, since n is large with unknown σ.The Student's t, since n is large with unknown σ.

(e) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(f) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(g) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence that Gentle Ben's glucose is higher than average.Fail to reject the null hypothesis, there is sufficient evidence that Gentle Ben's glucose is higher than average.     Reject the null hypothesis, there is insufficient evidence that Gentle Ben's glucose is higher than average.Reject the null hypothesis, there is sufficient evidence that Gentle Ben's glucose is higher than average.

12.Question DetailsMy Notes

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna referenced from: Hummingbirds, K. Long and W. Alther.) Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows:

Let x be a random variable representing weights of Anna's hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.74 gram. It is known (from previous research) that for the population of all Anna's hummingbirds, the average weight has been 4.25 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.25 grams? Use α = 0.05.

(a) Enter the following.
x =  
s =  
(b) Identify the claim, the null hypothesis, and the alternative hypothesis.

(c) Will you use a left-tailed, right-tailed, or two-tailed test?

two-tailedright-tailed    left-tailed

(d) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since n is large with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ.    The standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since n is large with unknown σ.The standard normal, since n is large with known σ.The standard normal, since we assume that x has a normal distribution with known σ.

(e) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(f) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(g) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that humming birds in the Grand Canyon weigh less.Reject the null hypothesis, there is sufficient evidence that humming birds in the Grand Canyon weigh less.    Fail to reject the null hypothesis, there is insufficient evidence that humming birds in the Grand Canyon weigh less.Reject the null hypothesis, there is insufficient evidence that humming birds in the Grand Canyon weigh less.

13.Question DetailsMy Notes

The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (J. P. Morgan, Bank of America, etc) gave the following P/E ratios.

Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Financial publications indicated that the P/E ratio of the S&P 500 stock index has typically been 18.6. Let x be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that x has a normal distribution and σ = 4.3. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18.6? Use α = 0.05.

(a) Enter the following.
x =  
s =  
(b) Identify the claim, the null hypothesis, and the alternative hypothesis.

(c) Will you use a left-tailed, right-tailed, or two-tailed test?

left-tailedtwo-tailed    right-tailed

(d) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ.    The standard normal, since n is large with unknown σ.The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since n is large with unknown σ.The standard normal, since n is large with known σ.

(e) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(f) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(g) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence that average P/E for large banks is less than the S&P 500 Index.Fail to reject the null hypothesis, there is sufficient evidence that average P/E for large banks is less than the S&P 500 Index.     Reject the null hypothesis, there is insufficient evidence that average P/E for large banks is less than the S&P 500 Index.Reject the null hypothesis, there is sufficient evidence that average P/E for large banks is less than the S&P 500 Index.

14.Question DetailsMy Notes

Nationally, about 10.3% of the total U.S. wheat crop is destroyed each year by hail. An insurance company is studying wheat hail damage claims in Weld County, Colorado. A random sample of 16 claims in Weld County reported the following percentages of their wheat lost to hail.

Let x be a random variable that represents the percentage of wheat crop in Weld County lost to hail. Assume that x has a normal distribution and σ = 4.0%. Do these data indicate that the percentage of wheat crop lost to hail in Weld County is different (either way) from the national mean of 10.3%? Use α = 0.10.

(a) Enter the following.
x =  %
s =  %
(b) Identify the claim, the null hypothesis, and the alternative hypothesis.

(c) Will you use a left-tailed, right-tailed, or two-tailed test?

two-tailedleft-tailed    right-tailed

(d) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ.    The standard normal, since n is large with known σ.The Student's t, since we assume that x has a normal distribution with known σ.The Student's t, since n is large with unknown σ.The standard normal, since n is large with unknown σ.

(e) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(f) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(g) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence that the average hail damage to wheat crops in Weld County differs from the national average.Fail to reject the null hypothesis, there is sufficient evidence that the average hail damage to wheat crops in Weld County differs from the national average.    Reject the null hypothesis, there is insufficient evidence that the average hail damage to wheat crops in Weld County differs from the national average.Reject the null hypothesis, there is sufficient evidence that the average hail damage to wheat crops in Weld County differs from the national average.

15.Question DetailsMy Notes

Total blood volume per body weight (ml/kg) is important in medical research. For healthy adults, the red blood cell volume mean is about 36.2 ml/kg. Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows.

Let x be a random variable that represents Roger's red blood cell volume. Assume that x has a normal distribution and σ = 4.80. Do the data indicate that Roger's red blood cell volume is different (either way) from 36.2 ml/kg? Use a 0.10 level of significance.

(a) Enter the following.
x =  
s =  
(b) Identify the claim, the null hypothesis, and the alternative hypothesis.

(c) Will you use a left-tailed, right-tailed, or two-tailed test?

two-tailedright-tailed    left-tailed

(d) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since n is large with unknown σ.The standard normal, since n is large with known σ.    The Student's t, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ.The standard normal, since we assume that x has a normal distribution with known σ.The standard normal, since n is large with unknown σ.

(e) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(f) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(g) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence that Roger's average red cell volume differs from the average for healthy adults.Fail to reject the null hypothesis, there is sufficient evidence that Roger's average red cell volume differs from the average for healthy adults.    Reject the null hypothesis, there is insufficient evidence that Roger's average red cell volume differs from the average for healthy adults.Reject the null hypothesis, there is sufficient evidence that Roger's average red cell volume differs from the average for healthy adults.

16.Question DetailsMy Notes

Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. From previous studies, it was determined that x has a distribution that is approximately normal. For the population of healthy female adults, the mean of the x distribution has been approximately 4.54. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are listed below. Do the given data indicate that the average RBC count for this patient is lower than 4.54? Use α = 0.05.

(a) Enter the following.
x =  
s =  
(b) Identify the claim, the null hypothesis, and the alternative hypothesis.

(c) Will you use a left-tailed, right-tailed, or two-tailed test?

right-tailedtwo-tailed    left-tailed

(d) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since n is large with unknown σ.The standard normal, since we assume that x has a normal distribution and σ is known.    The Student's t, since n is large with known σ.The standard normal, since we assume that x has a normal distribution and σ is unknown.The Student's t, since we assume that x has a normal distribution and σ is known.The Student's t, since we assume that x has a normal distribution and σ is unknown.

(e) Sketch the sampling distribution showing the area corresponding to the approximate P-value.

(f) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(g) State your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence that the average RBC count for this patient is less than 4.54.Fail to reject the null hypothesis, there is sufficient evidence that the average RBC count for this patient is less than 4.54.    Reject the null hypothesis, there is insufficient evidence that the average RBC count for this patient is less than 4.54.Reject the null hypothesis, there is sufficient evidence that the average RBC count for this patient is less than 4.54.

17.Question DetailsMy Notes

People gain weight when they take in more energy from food than they expend. Researchers wanted to investigate the link between obesity and energy spent on daily activity. Choose 20 healthy volunteers who don't exercise. Deliberately choose 10 who are lean and 10 who are mildly obese but still healthy. Attach sensors that monitor the subjects' every move for 10 days. The table below presents data on the time (in minutes per day) that the subjects spent standing or walking, sitting, and lying down. Is there a significant difference between the mean times the two groups spend lying down? Let μ1 be the mean time spent lying down by the lean group, and μ2 be the mean time for the obese group.

18.Question DetailsMy Notes

Recall that small effects may be statistically significant if the samples are large. A study of small-business failures looked at 151 food-and-drink businesses. Of these, 108 were headed by men and 43 were headed by women. During a three-year period, 15 of the men's businesses and 6 of the women's businesses failed.

(a) Find the proportions of failures for businesses headed by men (sample 1) and businesses headed by women (sample 2). These sample proportions are quite close to each other.

Give the P-value for the z test of the hypothesis that the same proportion of women's and men's businesses fail. (Use the two-sided alternative.) The test is very far from being significant. (Round your test statistic to two decimal places and your P-value to four decimal places.)

(b) Now suppose that the same sample proportions came from a sample of 30 times as large. That is, 180 out of 1290 business headed by women and 450 out of 3240 businesses headed by men fail. Verify that the proportions of failures are exactly the same as in (a). Repeat the z test for the new data, and show that it is now more significant. (Round your test statistic to two decimal places and your P-value to four decimal places.)

(c) Give the 95% confidence intervals for the difference between the proportions of men's and women's businesses that fail from Part (a) and Part (b).

(d) What is the effect of larger samples on the confidence interval?

The larger samples make the margin of error (and thus the length of the confidence interval) larger.The larger samples make the difference (and thus the length of the confidence interval) larger.    The larger samples make the difference (and thus the length of the confidence interval) smaller.The larger samples make the margin of error (and thus the length of the confidence interval) smaller.