Stats Homework

Show work on questions 8-1,8-3,8-4,8-6, everything else work does not need to be shown.

8-1)In the past the average time that it takes for a woman to complete the San Francisco Marathon was 4.62 hours. This year the average time for the 2001 women finishing the SF Marathon the average time was 4.29 hours with a standard deviation of 1.11 hours. Can it be concluded that this years average time for women to finish the SF Marathon is statistically significantly different from the past years' average time? (Use α = 5%) Select the best choice. Show your work for full credit.

a)      The claim of μ ≠ 4.62 hours with p-value = 2.44 and a 95% Conf. Int (4.24,4.34) means support Ho and reject the claim that the times are significantly different from the past times.

b)      The Ho of μ = 4.62 hours with p-value = 0 and a 95% Conf. Int (4.24,4.34) means support the Ho and reject the claim that the times are significantly different from the past times.

c)      The Ho of μ = 4.62 hours with p-value = 0 and a 95% Conf. Int (4.24,4.34) means support the Ho and reject the claim that the times are significantly different from the past times.

d)     The claim of μ = 4.62 hours with p-value = 0 and a 95% Conf. Int (4.24,4.34) means support the claim that the times are significantly different from the past times.

8-2) The Kaiser Medical Foundation reports that the cost to rehabilitate a football player following a head injury is at least $28,500. To test this claim a researcher surveys the medical billing records of 15 football players who were treated for head injuries. The average cost for rehabilitation in this randomly selected sample is $30,885  with a standard deviation of $1,123. Is the actual cost of rehabilitation $28,500 as Kaiser claims? First, state the null and alternative hypotheses for this hypothesis test.

a)       Ho: μ ≤ $28,500 and H1: μ > $28,500

b)       Ho: μ ≥ $28,500 and H1: μ < $28,500

c)       Ho: μ = $28,500 and H1: μ ≠ $28,500

d)      Ho: μ ≠ $28,500 and H1: μ = $28,500

What is the correct test to use in testing the above hypothesis test?

a)      Z – Test

b)      T – Test

c)      2 Samp Z Test

d)     2 Samp T Test

8-3) A sugar company packages sugar in 5 pound bags. An FDA food inspector suspects that the average amount of sugar in the 5 pound bags is actually at most 5 pounds on average. A simple random sample of 75 of the 5 pound bags results in a sample avarage of 4.95 lbs. with a standard deviation of 0.5 lbs. The inspector wishes to be 98% confident in his final determination about this company's packaging practices. Select the choice below that best sumarizes the FDA inspectors findings.

(Use the Show Work feature to receive full credit.)

a)      Ho: μ ≤ 5 and H1: μ > 5 ; p-value = .807, therefore reject the claim with 4.72 ≤ μ ≤ 4.98

b)      Ho: μ ≥ 5 and H1: μ < 5 ; p-value = .807, therefore support Ho and support the claim with 4.82 ≤ μ ≤ 5.08

c)      Ho: μ < 5 and H1: μ ≥ 5 ; p-value = .807, therefore reject Ho and support the claim with 4.72 ≤ μ ≤ 4.98

d)     Ho: μ ≤ 5 and H1: μ > 5 ; p-value = .807, therefore support Ho and support the claim with 4.82 ≤ μ ≤ 5.08

8-4) This year a study of student purchasing habits reported that 75% of graduating college seniors will have student load debt of more than $25,000. A dean of Student Services feels for her university and that the percentage is at least 75%. She surveys 200 graduating seniors. The dean finds that 125 seniors in this random sample will have student loan debt of more than $25,000. State the null and alternative hypotheses for this hypothesis test.

a)      Ho: μ < $25,000 and  H1: μ ≥ $25,000

b)      Ho: p ≤ .75 and H1: p > .75

c)      Ho: p > .75 and H1: p ≤ .75

d)     Ho: p ≥ .75 and H1: p < .75

For the hypothesis test above, select the best statement. α = 1%

(Show Work to receive full credit)

a)      p-value = 2.23 > α, therefore support Ho and support the claim.

b)      p-value = 0 ≤ α, therefore reject Ho and reject the claim.

c)      p-value = 1 ≥ α, therefore support Ho and support the claim.

d)     p-value = 0 ≤ α, therefore support Ho and support the claim.

8-5)The choices below all relate to the following hypothesis question.

A research sports medicine physician claims that athletes who train using "cardio workouts" on a regular basis have a maximum oxygen uptake equal to the average of all adults. To test his claim he randomly samples 15 "cardio workout" athletes and finds that the sample average is 42.3 ml/kg with a sample standard deviation of 6 ml/kg. If the average maximum oxygen uptake is 39 ml/kg for all adults, is there enough evidence to support this claim at α = .02?

Select the best choice for the null and alternative hypotheses.

a)      Ho: μ > 42.3  and H1: μ ≤ 42.3

b)      Ho: μ = 42.3  and H1: μ ≠ 42.3

c)      Ho: μ ≤ 39  and H1: μ > 39

d)     Ho: μ = 39  and H1: μ ≠ 39

For the above hypothesis test, select the best choice below. α = 2%

a)      p value > α, therefore Reject the claim.

b)      p value > α, therefore Support H0 and Reject the claim.

c)      p value > α, therefore Reject Ho and Reject the claim.

d)     p value > α, therefore Support Ho and Support the claim.

8-6)An education researcher believes that the dropout rate for high school seniors in California is 12%. To test this belief the researcher looks at a simple random sample of 500 senior high school seniors and finds that 72 seniors in this sample dropped out. For this hypothesis test, sellect the correct null and alternative hypotheses.

a)      Ho: μ ≠ 12% and H1: μ = 12%

b)      Ho: p = .12 and H1 p ≠ .12

c)      Ho: p > .12 and H1 p ≤ .12

d)     Ho: p ≤ .12 and H1 p > .12

For the hypothesis test above, which conclusion statement is correct fot a level of significance of 5%?

(Use the "Show Work" feature to receive full credit.)

a)      p - value ≤ α, therefore reject the claim.

b)      p - value ≤ α, therefore reject the Ho and support the claim.

c)      p - value > α, therefore support the Ho and reject the claim.

d)     p - value > α, therefore support the Ho and support the claim.

8-8) A researcher claims that the average annual salary of part-time community college instructors is  at most $45,000. To test this claim, a sample of 25 part-time community college instructors is selected at random. The sample average is $42,500 with a sample standard deviation of $3,100. State the null and alternative hypotheses for used to test this claim.

a)      Ho: μ ≤ $45,000 and H1: μ > $45,000

b)      Ho: μ < $45,000 and H1: μ ≥ $45,000

c)      Ho: μ ≥ $45,000 and H1: μ < $45,000

d)     Ho: μ > $45,000 and H1: μ ≤ $45,000

For the hypothesis question above, which hypothesis test should be used.

a)      Z – Test

b)      t – Test

c)      1 Prop Z Test

d)     2 Samp t Test

8-10)A researcher wishes to test the claim that the average age of Los Angeles County Lifegaurds is  at least 28 years old. To test the claim the researcher uses a sample of 50 randomly selected lifeguards from Los Angeles County and finds that the sample average and standard deviation are 29 years and 2.5 years respectively. What is the p-value for this hypothesis test to the nearest thousandth decimal place?

8-11)Find the p-value in a two tail T-Test when the test statistic (t value) is -1.523 and the sample size is 13.

                          _______ < p-value < ______ 

(Your answer should be two "decimals" in ascending order seperated by a comma)

8-12)Find the critical value for a left-tailed hypothesis test in which α = .02

Assume that this is a normal distribution.

Round your answer to the thousandth decimal place.

9-2) Health researchers surveyed people living in a large city and people living in the suburbs. Of the 250 city people surveyed, 187 had gotten flu shots. Of the 180 people living in the suburbs, 98 had gotten flu shots. What is the 90% Confidence Interval Estimate of the difference in the proportion (or percentage) of people receiving flu injection in the city and in the suburb? Give your answer as to four place decimals seperated by a comma.

9-7)Two surveys were done regarding credit card debt. Five years ago the average credit card debt was $8318. The average credit card debt for a recent year was $9205. Assume sample sizes of 35 were used and the standard deviations of both samples were $1928. Is there enough evidence to believe that the average credit card debt has changed in the past 5 years? Use a  0.05. Identify the null and alternative hypotheses, the p-value and the correct decision regarding the claim.

a)      Ho: μ1 = μ2 and H1: μ1 ≠ μ2 with p-value = .054 support the claim that credit card debt has changed.

b)      Ho: μ1 ≠ μ2 and H1: μ1 = μ2 with p-value = .054 support the claim that credit card debt has changed.

c)      Ho: μ1 < μ2 and H1: μ1 ≥ μ2 with p-value = .054 support the claim that credit card debt has increased.

d)     Ho: μ1 = μ2 and H1: μ1 ≠ μ2 with p-value = .054 reject the claim that credit card debt has changed.

Construct the 95% Confidence Interval estimate for the difference in the amount of credit card debt based on the two surveys above.

a)      1790 ≤ μ1 - μ2 ≤ -16.308

b)      -1790 ≤ μ1 - μ2 ≤ 16.308

c)      -1790 ≤ μ1 - μ2 ≤ -16.308

d)     1790 ≤ μ1 - μ2 ≤ 16.308

9-8)In a sample of 80 Americans, 65% wished that they were rich. In a sample of 90 Europeans, 70% wished that they were rich. Find the 99% confidence interval for the difference of the two proportions.

a)      .2353 ≤ p1 - p2 ≤ .1353

b)      -.2353 ≤ p1 - p2 ≤ -.1353

c)      -.2353 ≤ p1 - p2 ≤ .1353

d)     .2353 ≤ p1 - p2 ≤ -.1353

At a  0.01, is there a difference in the proportions?

a)      There is no statistical difference in the percentage of Americans and Europeans who wish that they were rich at α = .01.

b)      The percentage of Americans who wish that they were rich is statistically greater than the percentage of Europeans who wish that they were rich at α = .01.

c)      The percentage of Americans who wish that they were rich is statistically less than the percentage of Europeans who wish that they were rich at α = .01.

9-9) In San Jose a sample of 73 mail carriers showed that 30 had been bitten by an animal during one week. In San Francisco in a sample of 80 mail carriers, 56 had received animal bites. Is there a significant difference in the proportions? Use a  0.05. Find the 95% confidence interval for the difference of the two proportions.

a)      .4401 ≤ p1 - p2 ≤ .1380

b)      .4401 ≤ μ1 - μ2 ≤ .1380

c)      -.4401 ≤ p1 - p2 ≤ .1380

d)     -.4401 ≤ p1 - p2 ≤ -.1380

Sellect the correct statement below based on the data given in this problem.

a)      The rate of mail carriers being bitten in San Jose and San Francisco are statistically equal at α = 5%

b)      The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%

c)      The rate of mail carriers being bitten in San Jose is statistically greater than the rate San Francisco at α = 5%

10-1) The data below represent the number of years that an alumnus has been out school and the yearly contribution that alumnus to his/her college. Use the data to determine the equation of the regression line and then predict the amount of money an alumnus who has been out of college for 9 years will contribute to his/her college. (Round to the nearest dollar and include the $ in your answer.)

# of years (x):         5      8      10     14    18     22

contribution ($):    170   190   195   205  210   225

10-2a) Find the coefficient of determination given that the correlation coefficient = .69

(Give your answer as a decimal rounded to the ten thousandth decimal place.)

10-2b) Find the percent of the data that can be explained by the regression line and regression equation given that the correlation coefficient = .69

(Give your answer as a percent rounded to the hundredth decimal place. Include the % sign)

10-5) Compute the value of the correlation coefficient for the data given below in a study of age and blood preasure. (Round your answer to three decimal places.)

Subject           Age           Blood Preasure

    A                  34                   128                   

    B                  35                   125          

    C                  41                   130                    

    D                  53                   135         

    E                  58                   140  

    F                  67                   145     

11-4) For the past year, national percentages of people's preference in car color are as follows:

White 35%, Silver 28%, Blue 24%, Red 10%, Other 3%

Of the 9,000 people who bought cars in San Jose recently, the following is the record of  colors:

White 3,145; Silver 2510; Blue 2,165; Red 905; Other 275

Use the "Goodness of Fit Test" and the Chi Square distribution to answer the following.

What is the value of the Chi Square Test Statistics for this problem to the nearest third decimal place?

M-2) A sociologist wanted to determine whether there was a difference in the amount of time children aged 57 spent watching television each day. Check the following data for evidence that the number of minutes spent watching television is equally distributed throughout the week. Then make the best choice from those given below.

Sunday    Monday    Tuesday    Wednesday   Thursday   Friday    Saturday

  200         112             123            130               160           225        247

What is the null hypothesis?

a)      Children spend different amounts of time watching TV each day.

b)      Children spend less time watching TV on school nights.

c)      Children spend the same amount of time watching TV each day.

d)     Children watch more TV on weekends.

For the hypothesis test above, make the best choice based on the Chi Square distribution and the Goodness of Fit test.

a)      The Chi Sq statistic = 100.1, p-value = 2.39 therefore support Ho and conclude that children watch the same amount of TV each day of the week.

b)      The Chi Sq statistic = 100.1, p-value = 2.39 therefore support Ho and conclude that children do not watch the same amount of TV each day of the week.

c)      The Chi Sq statistic = 100.1, p-value = 0, therefore support Ho and conclude that children do not watch the same amount of TV each day of the week.

d)     The Chi Sq statistic = 100.1, p-value = 0, therefore reject Ho and conclude that children do not watch the same amount of TV each day of the week.

M-3) Compute the value of the slope of the regression line for the data given below in a study of age and blood preasure. (Round your answer to three decimal places.)

Subject           Age           Blood Preasure

    A                  34                   115                   

    B                  35                   120          

    C                  41                   122                    

    D                  53                   130         

    E                  58                   140   

    F                  67                   145     

M-4) The data below represent the number of years that an alumnus has been out school and the yearly contribution that alumnus to his/her college. Use the data to determine the equation of the regression line and then predict the amount of money an alumnus who has been out of college for 7.5 years will contribute to his/her college. (Round to the nearest dollar and include the $ in your answer.)

# of years (x):         5      8      10     14    18     22

contribution ($):    170   190   195   205  210   225

M-5a) Find the coefficient of determination given that the correlation coefficient = .58

(Give your answer as a decimal rounded to the ten thousandth decimal place.)

M-5b) Find the percent of the data that can be explained by the regression line and regression equation given that the correlation coefficient = .58

(Give your answer as a percent rounded to the hundredth decimal place. Include the % sign)

M-6) Compute the value of the correlation coefficient for the data given below in a study of age and blood preasure. (Round your answer to three decimal places.)

Subject           Age           Blood Preasure

    A                  44                   128                    

    B                  45                   125          

    C                  51                   130                    

    D                  63                   135         

    E                  68                   140  

    F                  77                   145     

M-11) In a sample of 80 Americans, 65% wished that they were rich. In a sample of 90 Europeans, 60% wished that they were rich. Find the 99% confidence interval for the difference of the two proportions.

a)      .1412 ≤ p1 - p2 ≤ .2412

b)      -.1412 ≤ p1 - p2 ≤ -.2412

c)      -.1412 ≤ p1 - p2 ≤ .2412

d)     .1412 ≤ p1 - p2 ≤ -.2412

At a  0.01, is there a difference in the proportions?

a)      There is no statistical difference in the percentage of Americans and Europeans who wish that they were rich at α = .01.

b)      The percentage of Americans who wish that they were rich is statistically greater than the percentage of Europeans who wish that they were rich at α = .01.

c)      The percentage of Americans who wish that they were rich is statistically less than the percentage of Europeans who wish that they were rich at α = .01.

M-12) Health researchers surveyed people living in a large city and people living in the suburbs. Of the 250 city people surveyed, 187 had gotten flu shots. Of the 180 people living in the suburbs, 98 had gotten flu shots. What is the 90% Confidence Interval Estimate of the difference in the proportion (or percentage) of people receiving flu injection in the city and in the suburb? Give your answer as to four place decimals seperated by a comma.

M-16) Find the critical value for α = .05 with the n = 25 in a two tailed hypothesis test.

(Hint: There are two answers. Give the answers in ascending order seperated by a comma)

M-17a) An education researcher claims the the average daily salary for substitute teachers in Santa Clara County is NOT $72 per day. A random sample of ten Santa Clara County school districts is sellected and the daily salaries (in dollars) are listed below. Calculate the p-value for this hypothesis test.(Express your answer as a decimal rounded to the hundredth decimal place)

68  72  66  70  75  72  66  69  71  78

M-17b) For the hypothesis test above, what is the ctritical value for α = 10%?

M-18) A researcher wishes to test the claim that the average age of Los Angeles County Lifegauds is  at most 28 years old. To test the claim the researcher uses a sample of 50 randomly selected lifeguards from Los Angeles County and finds that the sample average and standard deviation are 29 years and 2.5 years respectively. What is the p-value for this hypothesis test to the nearest thousandth decimal place?

M-20) Find the p-value in a left tail T-Test when the test statistic (t value) is -2.345 and the sample size is 11.

 _______ < p-value < ______   

(Your answer should be two "decimals" in ascending order seperated by a comma)