Exam 12: Inferences for Population Proportions

Use the two-proportions z-test to perform the required hypothesis test. Assume that independent simple randomsamples have been selected from the two populations. Use the critical-value approach. -Of 85 randomly selected women, 38 have tried some form of alternative medicine. Of 90 randomly selected men, 23 have tried some form of alternative medicine. At the 1% significance level, do the data provide sufficient evidence to conclude that women are more likely than men to try alternative forms of medicine?

A two-proportions z-test is to be performed using the P-value approach. Use the given sample data to find the P-valuefor the hypothesis test. - $\mathrm { x } _ { 1 } = 11 , \mathrm { n } _ { 1 } = 200 , \mathrm { x } _ { 2 } = 8 , \mathrm { n } _ { 2 } = 100 ; \mathrm { H } _ { 0 } : \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 } , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } _ { 1 } \neq \mathrm { p } _ { 2 } , \alpha = 0.01$

The number of successes and the sample size are given for a simple random sample from a population. Determine the sample proportion, $\hat { p }$ . -x = 69, n = 125

Use the two-proportions z-test to perform the required hypothesis test. Assume that independent simple randomsamples have been selected from the two populations. Use the P-value approach. -7 of 8500 people vaccinated against a certain disease later developed the disease. 18 of 10,000 people vaccinated with a placebo later developed the disease. At the 2% significance level, do the data provide sufficient evidence to conclude that those who are vaccinated against the disease are at lower risk of developing the disease than those vaccinated with a placebo?

Use the two-proportions z-test to perform the required hypothesis test. Assume that independent simple randomsamples have been selected from the two populations. Use the critical-value approach. -A report on the nightly news broadcast stated that 15 out of 112 households with pet dogs were burglarized and 21 out of 187 without pet dogs were burglarized. At the 5% significance level, do the data provide sufficient evidence to conclude that households with pet dogs are at less risk of being burglarized?

You are planning to use a sample proportion $\hat { p }$ to estimate a population proportion, p. True or false, the sample proportion for a sample of size 100 is more likely to lie within $0.01$ of the population proportion than the sample proportion for a sample of size 200?

Use the one-proportion z-test to perform the required hypothesis test. Use the critical-value approach. -A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and that production is not really out of control. At the 0.01 level of significance, do the data provide sufficient evidence that the percentage of defects exceeds 3%?

The numbers of successes and the sample sizes are given for independent simple random samples from two populations.Decide whether using the two-proportions z-procedures is appropriate. - $\mathrm { x } _ { 1 } = 44 , \mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 2 } = 20 , \mathrm { n } _ { 2 } = 24$

A mayoral election race is tightly contested. In a random sample of 1400 likely voters, 742 said that they were planning to vote for the current mayor. Based on this sample, would you claim that the mayor will win a majority of the votes? Explain.

Use the one-proportion z-test to perform the required hypothesis test. Use the critical-value approach. -An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 237 fathers from Littleton yielded 102 who did not help with child care. Do the data provide sufficient evidence to conclude that in Littleton the proportion of fathers who take no responsibility for child care.is higher than 0.34? Use a 0.05 significance level.

The number of successes and the sample size are given for a simple random sample from a population. Decide whetherusing the one-proportion z-interval procedure is appropriate. -x = 77, n = 120

The number of successes and the sample size are given for a simple random sample from a population. Decide whetherusing the one-proportion z-interval procedure is appropriate. -x = 5, n = 51

$\text { Find the required sample size without making a guess for the observed value of } \hat { p } \text {. }$ -A manufacturer of kitchen utensils wishes to estimate the proportion of left handed people in the population. Obtain a sample size that will ensure a margin of error of at most 0.046 for a 93% Confidence interval.

Use the two-proportions z-test to perform the required hypothesis test. Assume that independent simple randomsamples have been selected from the two populations. Use the P-value approach. - Use the given sample data to test the claim that < . Use a significance level of 0.10 . =84=95

Use the one-proportion z-interval procedure to find the required confidence interval. -A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the proportion of all New York State union Members who favor the Republican candidate.

Let p1 represent the proportion of men in a city who are unemployed and let p2 represent the proportion of women in the same city who are unemployed. A 95% confidence interval for p1 - p2 is from -0.05 to -0.03. Give an interpretation of this confidence interval.

Use the two-proportions z-test to perform the required hypothesis test. Assume that independent simple randomsamples have been selected from the two populations. Use the critical-value approach. -A researcher finds that of 1000 people who regularly attend a religious service, 31 would stop to help a person with car trouble. Of 1200 people interviewed who do not regularly attend a religious service, 22 would stop to help a person with car trouble. At the 0.05 significance level, do the data provide sufficient evidence to conclude that those who regularly attend a religious service are more likely to stop and help a person with car trouble?

Suppose the proportion of women who follow a regular exercise program is pw and the proportion of men who follow a regular exercise program is pm. A study found a 90% confidence interval for pw - pm to be (-0.021, 0.112). Does this study provide evidence that the proportion of women who exercise is different from the proportion of men who exercise? Explain.

Use the one-proportion z-test to perform the required hypothesis test. Use the critical-value approach. -In 2000, the percentage of adults in a certain town who drove an SUV was 53%. In 2005, in a random sample of 100 people from this town, 45% said that they drive an SUV. At the 10% level of significance, do the data provide sufficient evidence to conclude that the percentage of adults in this town who drive an SUV has changed from the 2000 percentage of 53%?

Use the two-proportions z-test to perform the required hypothesis test. Assume that independent simple randomsamples have been selected from the two populations. Use the P-value approach. -A researcher finds that of 1000 people who regularly attend a religious service, 31 would stop to help a person with car trouble. Of 1200 people interviewed who do not regularly attend a religious service, 22 would stop to help a person with car trouble. At the 0.05 significance level, do the data provide sufficient evidence to conclude that those who regularly attend a religious service are more likely to stop and help a person with car trouble?