(a) Write the claim mathematically and identify H0 and Ha. (b) Find the critical value(s) and identify the rejection region(s). (c) Find the...

3. (a) Write the claim mathematically and identify H0 and Ha. (b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the null hypothesis.

An environmental agency recently claimed more than 30% of consumers have stopped buying a certain product because of environmental concerns. In a random sample of 1040 consumers, you find 35% have stopped buying the product. At alphaαequals=0.01, do you have enough evidence to support the claim?

4. A humane society claims that less than 39% of U.S. households own a dog. In a random sample of 399 U.S. households, 154 say they own a dog. At alphaαequals=0.04 is there enough evidence to support the society's claim?

(a) Write the claim mathematically and identify H0 and Ha. (b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

5. You interview a random sample of 50 adults. The results of the survey show that 48% of the adults said they were more likely to buy a product when there are free samples. At alphaαequals=0.05, can you reject the claim that at least 55% of the adults are more likely to buy a product when there are free samples?

12. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table shows the shoe size and heights (in) for 6 men.

a) x=size 11.5

(b) x=size 10.5

(d) x=size 7.5

Shoe size, x Height, y

7.0 65.0

8.0 67.0

9.0 73.0

11.0 73.0

12.5 74.0

13.0 74.0

11. The accompanying data are the length (in centimeters) and girths (in centimeters) of 12 harbor seals. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not.

(a) x=140 cm

(b) x=172 cm

(d) x=158 cm

Length, x Girth, y

137 105

168 131

153 116

146 106

158 125

158 118

124 102

136 104

154 120

147 109

147 107

146 108

10. For the following data (a) display the data in a scatter plot, (b) calculate the sample correlation coefficient r, and (c) make a conclusion about the type of correlation. Use technology.

The altitudes (in thousands of feet) and speeds of sound (in feet per second) at these altitudes are shown in the data set below.

Altitude,_x Speed_of_sound,_y

0 1117.4

5 1097.3

10 1077.4

15 1057.9

20 1037.6

25 1015.6

30 996.3

35 970.4

40 967.1

45 967.1

50 967.1

16. Find the expected frequency, Ei, for the given values of n and pi.

n=230, pi=0.39

19. Use the contingency table to the right to calculate the marginal frequencies and find the expected frequency for each cell in the contingency table. Assume that the variables are independent.

Gender Compact Full-size SUV Van

Male 17 28 16 21

Female 10 16 56 19

Calculate the marginal frequencies and sample size.

Find the expected frequency for each cell in the contingency table.

24. Find the critical F-value for a right-tailed test using the indicated level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.05

d.f.N=3,

d.f.D=25

25. Find the critical F-value for a right-tailed test using the indicated level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.01

d.f.N=3,

d.f.D=19

26. Find the critical F-value for a two-tailed test using the indicated level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.01,

d.f.N=9,

d.f.D=9

28. The table below shows a sample of waiting times (in days) for a heart transplant for two age groups. At α=0.05, can you conclude that the variances of the waiting times differ between the two age groups?

18-34 35-49

160 212

172 191

170 209

171 205

161 198

213

200

Determine the hypotheses. Let sigma 2σ2/1 be the variance for the 18-34 group and let sigma t 2σ2/2 be the variance for the 35-49 group.

Determine the critical value.

What is the rejection region for this F-test?

Compute the F test statistic

Reach a decision. (Reject/do not reject H0. There is enough/not enough evidence to conclude that the variances of the waiting times differ between the two age groups.

20. The contingency table shows how a random sample of college freshmen graded the leaders of three types of institutions. At α=0.10, can you conclude that the grades are related to the institution?

Institution A B C D/F

Military 21 43 15 18

Religious 21 47 29 15

Media / Press 17 27 40 20

Identify the claim and state the null and alternative hypotheses

Determine the degrees of freedom, find the critical value, and identify the rejection region.

Calculate the test statistic.

Decide to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim.