4.) Since an instant replay system for tennis was introduced at a majortournament, men challenged 1400 refereecalls, with the result that 412 of the calls were overturned. Women challenged 754 refereecalls, and 230 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts(a) through(c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesistest?

A.

H0: p1p2

H1: p1p2

B.

H0: p1p2

H1: p1p2

C.

H0: p1=p2

H1: p1p2

D.

H0: p1=p2

H1: p1

E.

H0: p1=p2

H1: p1>p2

F.

H0: p1p2

H1: p1=p2

b. Test the claim by constructing an appropriate confidence interval.

c. Based on theresults, does it appear that men and women may have equal success in challengingcalls?

Review the conclusions made based on the hypothesis test and the confidence interval. Use this information to determine whether men and women may have equal success in challenging calls.

5.) A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 286 people over the age of55, 70 dream in black andwhite, and among 313 people under the age of25, 12 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts(a) through(c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesistest?

A.

H0: p1=p2

H1: p1

B.

H0: p1p2

H1: p1p2

C.

H0: p1=p2

H1: p1p2

D.

H0: p1=p2

H1: p1>p2

E.

H0: p1p2

H1: p1p2

F.

H0: p1p2

H1: p1=p2

b. Test the claim by constructing an appropriate confidence interval.

c. An explanation given for the results is that those over the age of 55 grew up exposed to media that was mostly displayed in black and white. Can these results be used to verify thatexplanation?

8.)Data on the weights(lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Complete parts(a) and(b) below. Use a 0.01 significance level for both parts.

Diet Regular

1 2

n 23 23

x 0.79544 lb 0.81204 lb

s 0.00448 lb 0.00743 lb

a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.

What are the null and alternativehypotheses?

A.

H0: 1=2

H1: 1>2

B.

H0: 1=2

H1: 1<2

C.

H0: 1=2

H1: 12

D.

H0: 12

H1: 1< 2

find the teststatistic: t=_______

TheP-value is: P=_________

b. Construct a confidence interval appropriate for the hypothesis test in part(a).

Use this information to interpret the confidence interval and compare it to the conclusion of the hypothesis test.

9.) A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Complete parts(a) and(b) below. Use a 0.05 significance level for both parts.

Treatment Placebo

1 2

n 33 36

x 2.34 2.64

s 0.97 0.63

a. Test the claim that the two samples are from populations with the same mean.

What are the null and alternativehypotheses?

A.

H0: 1<2

H1: 12

B.

H0: 1=2

H1: 12

C.

H0: 12

H1: 1<2

D.

H0: 1=2

H1: 1>2

find the teststatistic: t=_______

TheP-value is: P=_________

b. Construct a confidence interval appropriate for the hypothesis test in part(a).

Use this information to interpret the confidence interval and compare it to the conclusion of the hypothesis test.

10.) Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment(with magnets) group and the sham(or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Complete parts(a) and(b) below.

Treatment Sham

1 2

n 13 13

x 0.55 0.38

s 0.99 1.42

a.Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

What are the null and alternativehypotheses?

A.

H0: 1=2

H1: 12

B.

H0: 1<2

H1: 12

C.

H0: 12

H1: 1<2

D.

H0: 1=2

H1: 1

find the teststatistic: t=_______

TheP-value is: P=_________

Is it valid to argue that magnets might appear to be effective if the sample sizes arelarger?

Determine what effect a larger sample size will have on the test statistic and theP-value. Use the conclusion from the original hypothesis test to answer the question.

b. Construct a confidence interval suitable for testing the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

11.) A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Complete parts(a) and(b) below.

Men Women

1 2

n 11 59

x 97.66F 97.42F

s 0.82F 0.65F

a. Use a 0.01 significance level to test the claim that men have a higher mean body temperature than women.

What are the null and alternativehypotheses?

A.

H0: 12

H1: 1<2

B.

H0: 12

H1: 1<2

C.

H0: 1=2

H1: 1>2

D.

H0: 1=2

H1: 1 2

find the teststatistic: t=_______

TheP-value is: P=_________

b. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.

Use this information to interpret the confidence interval and compare it to the conclusion of the hypothesis test.

12.) Listed in the data table are IQ scores for a random sample of subjects with medium lead levels in their blood. Also listed are statistics from a study done of IQ scores for a random sample of subjects with high lead levels. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts(a) and(b) below.

Medium Lead Level High Lead Level

72 n=11

85 x2=88.561

92 s2= 9.719

85

85

97

83

92

95

111

91

a. Use a 0.01 significance level to test the claim that the mean IQ scores for subjects with medium lead levels is higher than the mean for subjects with high lead levels.

What are the null and alternativehypotheses? Assume that population 1 consists of subjects with medium lead levels and population 2 consists of subjects with high lead levels.

A.

H0: 12

H1: 1>2

B.

H0: 12

H1: 1>2

C.

H0: 1=2

H1: 12

D.

H0: 1=2

H1: 1>2

Use technology to find the value of x1, rounding to three decimal places.

Use technology to find the value of s1, rounding to three decimal places.

Identify the value of n1.

Enter the calculated and given values of x1, x2, s1, s1, n1, and n2 into technology and perform the appropriate test. Read the value of the test statistic t from the technologyoutput, rounding to two decimal places.

t=

P-value=

b. Construct a confidence interval suitable for testing the claim that the mean IQ scores for subjects with medium lead levels is higher than the mean for subjects with high lead levels.

Use this information to interpret the confidence interval and compare it to the conclusion of the hypothesis test.

13.)Listed below are time intervals(min) between eruptions of a geyser. Assume that the"recent" times are within the past fewyears, the"past" times are from around 20 yearsago, and that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Does it appear that the mean time interval haschanged? Is the conclusion affected by whether the significance level is 0.10 or 0.01?

Recent

77

92

90

80

56

101

61

87

69

89

81

83

56

80

75

102

61

Past

89

87

93

94

63

85

84

92

88

91

91

Let 1 be the recent times and let 2 be the past times. What are the null and alternativehypotheses?

A.

H0: 1=2

H1: 12

B.

H0: 12

H1: 1=2

C.

H0: 1<2

H1: 1=2

D.

H0: 1=2

H1: 1>2

t=________

Similarly, identify theP-value returned by thetest, which is labeledP, rounding to three decimal places.

P-value=____________

To reach a conclusion about the nullhypothesis, compare thisP-value to the significance level . If P-value, reject H0 and conclude that there is sufficient evidence to support the claim that the mean time interval has changed. If P-value>, fail to reject H0.

Lastly, perform the test again using the significance level =0.01. Then, compare the results and determine whether the choice of significance level makes a difference in the conclusion of the hypothesis test.