# stat 200 week 7 complete solution

2. The formula for a regression equation is Y’ = 2X + 9.

a. What would be the predicted score for a person scoring 6 on X?

b. If someone’s predicted score was 14, what was this person’s score on X?

6. For the X,Y data below, compute:

a. r and determine if it is signiﬁcantly different from zero.

b. the slope of the regression line and test if it differs signiﬁcantly from zero.

c. the 95% conﬁdence interval for the slope.

X

Y

4

6

3

7

5

12

11

17

10

9

14

21

5. At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem random to you. You think that it is a little fishy that sophomores organized the raffle and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors.

a. What are the expected frequencies of winners from each class?

b. Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi square and p values.

c. What do you conclude?

14. True/false: If the slope of a simple linear regression line is statistically signiﬁcant, then the correlation will also always be signiﬁcant.

70. The standard deviation of the chi-square distribution is twice the mean.

102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance.

French Toast

Pancakes

Waffles

Omelets

Men

47

35

28

53

Women

65

59

55

60

Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

113. df = ________

117. Let α = 0.05 Decision: ________

Conclusion (write out in a complete sentence.): ________

66. Can a coefficient of determination be negative? Why or why not?

Use the following information to answer the next two exercises. The cost of a leading liquid laundry detergent in different sizes is given in Table 12.31.

Size (ounces)

Cost ($)

Cost per ounce

16

3.99

32

4.99

64

5.99

200

10.99

82.

a. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatter plot.

b. Does it appear from inspection that there is a relationship between the variables? Why or why not?

c. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx

d. Find the correlation coefficient. Is it significant?

e. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.

f. If the laundry detergent were sold in a 90-ounce size, find the estimated cost.

g. Does it appear that a line is the best way to fit the data? Why or why not?

h. Are there any outliers in the given data?

i. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why

or why not?

j. What is the slope of the least-squares (best-fit) line? Interpret the slope.

1** Improving the productivity of chickens**. Farmers have discovered that more domestic chickens peck at objects placed in their environment, the healthier and more productive the chickens seem to be. White string has been found to be a particularly attractive pecking stimulus. In one experiment,

**chickens were exposed to be a sting stimulus. Instead white sting, blue-colored string was used. The number of pecks each chicken took at the blue string over a specified time interval was recorded. Summary statistics for the**

*72***chickens were**

*72***pecks,**

*x(bar)=1.13***pecks (**

*s= 2.21**Applied Animal Behavior Science, Oct. 2008*).

Previous research has shown that ** μ=7.5** pecks if chickens are exposed to white string. Conduct a test (at

**) to determine if the true mean number of pecks at blue string is less than**

*α=.01***pecks.**

*μ=7.5***Answers that come straight from program software packages will not be accepted.**

(a) (6 points) Formulate the null and the alternative hypothesis.

(b)(6 points) State and calculate the test statistics from the data.

(c) (6 points) Calculate the P-value.

(d) (6 points) Draw a conclusion.

2. A five-year-old census recorded that 20% of the families in a large community lived below the poverty level. To determine if this percentage has changed, a random sample of 400 families is studied and 70 are found to be living below the poverty level. Does this finding indicate that the current percentage of families earning incomes below the poverty level has changed from what it was five years ago? Test with α=0.05.

**Answers that come straight from program software packages will not be accepted.**

(a) (6 points) Formulate the null and the alternative hypothesis.

(b)(6 points) State and calculate the test statistics from the data.

(c) (6 points) Calculate the P-value.

(d) (6 points) Draw a conclusion.

3. A city health department wishes to determine if the mean bacteria count per unit volume of water at a lake beach is within the safety level of 200. A researcher collected 10 water samples of unit volume and found the bacteria counts to be

175, 190, 205, 193, 184, 207, 204, 193, 196, 180

Do the data strongly indicate that there is no cause for concern? Test with α=0.05.

**Answers that come straight from program software packages will not be accepted.**

(a) (6 points) Formulate the null and the alternative hypothesis.

(b)(6 points) State and calculate the test statistics from the data.

(c) (6 points) Calculate the P-value.

(d)(6 points) Draw a conclusion.

4. (8 points) A limnologist wishes to estimate the mean phosphate content per unit volume of the lake water. It is known from studies in previous years that the standard deviation has a fairly stable value of σ=4. How many water samples must the limnologist analyze to be 90% certain that the error of estimation does not exceed 0.8 milligrams?

**Answers that come straight from program software packages will not be accepted.**