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1. Newly purchased automobile tires of...

1. Newly purchased automobile tires of a certain type are supposed to be filled to a pressure of 34psi. Let μ denote the true average pressure. A test of H0: μ = 34 versus Ha: μ ≠ 34. Determine the value of the test statistic and the corresponding p-value in each of the following cases:

a) n=43, xbar=34.43, s=2.53

b)n=43, xbar=33.57 s=2.53

c)n=60, xbar=33.2, s=2.05

d)n=100, xbar= 34.38, s=1.8

2. In a study of a viral disease, researchers wish to know if the viral infection elevates body temperature. We know that the mean healthy body temperature in the general population is 37oC. A group of 35 patients suffering from this virus have their temperatures taken. We observe that their mean temperature is 37.5 oC and their SD is 1.0 oC. Use these data to determine whether the viral infection elevates body temperature at the 0.05 significance level.

3. A pain-killing drug was tested for efficacy in 70 women who were experiencing uterine cramping pain following childbirth. Thirty-five of the women were randomly allocated to receive the drug, and the remaining 35 received a placebo (inert substance). Capsules of drug or placebo were given before breakfast and again at noon. A pain relief score, based on hourly questioning throughout the day, was computed for each woman. The possible pain relief scores ranged from 0 (no relief) to 56 (complete relief for 8 hours). Summary results are shown in the table.

Treatment n

Placebo 35 31.96 12.05

Drug 35 25.32 13.78

Conduct a statistical hypothesis test for efficacy of the drug at reducing uterine cramping pain at the 0.01 significance level

4. Exercise 9.48 (p. 377) Hormone Therapy and Alzheimer’s Disease. In the last few years, many research studies have shown that the purported benefits of hormone replacement therapy (HRT) do not exist, and in fact, hormone replacement therapy actually increases the risk of several serious diseases. A four-year experiment involving 4,532 women, reported in The Press Enterprise, was conducted at 39 medical centers. Half of the women took placebos, and half took Prempro, a widely prescribed type of hormone replacement therapy. There were 40 cases of dementia in the hormone group and 21 in the placebo group. Is there sufficient evidence to indicate that the risk of dementia is higher for patients using Prempro? Test at the 1% level of significance.

5. Exercise 9.35 (p. 372) Early Detection of Breast Cancer. Of those women who are diagnosed to have early-stage breast cancer, one third eventually die of the disease. Suppose a community public health department instituted a screening program to provide for the early detection of breast cancer and to increase the survival rate p of those diagnosed to have the disease. A random sample of 200 women was selected from among those who were periodically screened by the program and who were diagnosed to have the disease. Let x represent the number of those in the sample who survive the disease.

a.)If you wish to detect whether the community screening program has been effective, state the null hypothesis that should be tested.

b.) State the alternative hypothesis.

c.) If 164 women in the sample of 200 survive the disease, can you conclude that the community screening program was effective? Test using α= .05 and explain the practical conclusions from your test.

d.) Find the p-value for the test and interpret it

6. Exercise 9.80 (p. 383) Breaststroke Swimmers. How much training time does it take to become a world class breaststroke swimmer? A survey published in The American Journal of Sports Medicine reported that the number of meters per week swum by two groups of swimmers –those who competed only in breaststroke and those who competed in the individual medley (which includes breaststroke). The number of meters per week practicing the breaststroke swim was recorded and the summary statistics are shown below.

Breaststroke Individual Medley

Sample Size 130 80

Sample Mean 9017 5853

Sample Standard Deviation 7162 1961

7. Exercise 9.81 (0. 383) Breaststroke, continued. Refer to exercise 9.80

a.) Construct a 99% confidence interval for the difference in the average number of meters swum by breaststroke versus individual medley swimmers.

b.) How much longer do pure breaststroke swimmers practice that stroke than individual medley swimmers? What is the practical reason for this difference?

a) n=43, xbar=34.43, s=2.53

b)n=43, xbar=33.57 s=2.53

c)n=60, xbar=33.2, s=2.05

d)n=100, xbar= 34.38, s=1.8

2. In a study of a viral disease, researchers wish to know if the viral infection elevates body temperature. We know that the mean healthy body temperature in the general population is 37oC. A group of 35 patients suffering from this virus have their temperatures taken. We observe that their mean temperature is 37.5 oC and their SD is 1.0 oC. Use these data to determine whether the viral infection elevates body temperature at the 0.05 significance level.

3. A pain-killing drug was tested for efficacy in 70 women who were experiencing uterine cramping pain following childbirth. Thirty-five of the women were randomly allocated to receive the drug, and the remaining 35 received a placebo (inert substance). Capsules of drug or placebo were given before breakfast and again at noon. A pain relief score, based on hourly questioning throughout the day, was computed for each woman. The possible pain relief scores ranged from 0 (no relief) to 56 (complete relief for 8 hours). Summary results are shown in the table.

Treatment n

Placebo 35 31.96 12.05

Drug 35 25.32 13.78

Conduct a statistical hypothesis test for efficacy of the drug at reducing uterine cramping pain at the 0.01 significance level

4. Exercise 9.48 (p. 377) Hormone Therapy and Alzheimer’s Disease. In the last few years, many research studies have shown that the purported benefits of hormone replacement therapy (HRT) do not exist, and in fact, hormone replacement therapy actually increases the risk of several serious diseases. A four-year experiment involving 4,532 women, reported in The Press Enterprise, was conducted at 39 medical centers. Half of the women took placebos, and half took Prempro, a widely prescribed type of hormone replacement therapy. There were 40 cases of dementia in the hormone group and 21 in the placebo group. Is there sufficient evidence to indicate that the risk of dementia is higher for patients using Prempro? Test at the 1% level of significance.

5. Exercise 9.35 (p. 372) Early Detection of Breast Cancer. Of those women who are diagnosed to have early-stage breast cancer, one third eventually die of the disease. Suppose a community public health department instituted a screening program to provide for the early detection of breast cancer and to increase the survival rate p of those diagnosed to have the disease. A random sample of 200 women was selected from among those who were periodically screened by the program and who were diagnosed to have the disease. Let x represent the number of those in the sample who survive the disease.

a.)If you wish to detect whether the community screening program has been effective, state the null hypothesis that should be tested.

b.) State the alternative hypothesis.

c.) If 164 women in the sample of 200 survive the disease, can you conclude that the community screening program was effective? Test using α= .05 and explain the practical conclusions from your test.

d.) Find the p-value for the test and interpret it

6. Exercise 9.80 (p. 383) Breaststroke Swimmers. How much training time does it take to become a world class breaststroke swimmer? A survey published in The American Journal of Sports Medicine reported that the number of meters per week swum by two groups of swimmers –those who competed only in breaststroke and those who competed in the individual medley (which includes breaststroke). The number of meters per week practicing the breaststroke swim was recorded and the summary statistics are shown below.

Breaststroke Individual Medley

Sample Size 130 80

Sample Mean 9017 5853

Sample Standard Deviation 7162 1961

7. Exercise 9.81 (0. 383) Breaststroke, continued. Refer to exercise 9.80

a.) Construct a 99% confidence interval for the difference in the average number of meters swum by breaststroke versus individual medley swimmers.

b.) How much longer do pure breaststroke swimmers practice that stroke than individual medley swimmers? What is the practical reason for this difference?

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