Exam 21: Comparing Two Proportions

A two-sample z-test for two population proportions is to be performed using the P-value approach.The null hypothesis is : = and the alternative is : ≠ .Use the given sample data to find the P-value for the hypothesis test.Give an interpretation of the p-value. -A poll reported that 41 of 100 men surveyed were in favour of increased security at airports,while 35 of 140 women were in favour of increased security.

A two-sample z-test for two population proportions is to be performed using the P-value approach.The null hypothesis is : = and the alternative is : ≠ .Use the given sample data to find the P-value for the hypothesis test.Give an interpretation of the p-value. -A poll reported that 30% of 60 Canadians between the ages of 25 and 29 had started saving money for retirement.Of the 40 Canadians surveyed between the ages of 21 and 24,25% had started saving for retirement.

An Ontario study examined the effect of day care on behavior in toddlers.Randomly selected parents who had a toddler in full-time day care were asked if their child had behavioral problems.The researchers found that among 987 parents surveyed,212 said their child had behavioral problems.Among 349 randomly selected parents with a toddler at home,17 reported that their child had behavioral problems.

You wish to construct a 90% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.04,what sample size should we take from each group? Assume equal sample sizes.

Suppose the proportion of women who watch CBC News is And the proportion of men who watch CBC News is .The survey found a 95% confidence interval for - Is (-0.06,0.25).Give an interpretation of this confidence interval.

A marketing survey involves product recognition in Ontario and British Columbia.Suppose the proportion of Ontario residents who recognized a product is And the proportion of British Columbia residents who recognized the product is .The survey found a 98% confidence interval for - Is (-0.023,-0.019).Give an interpretation of this confidence interval.

Use the given sample data to test the claim that p₁ < p₂.Use a significance level of 0.10. n₁ = 462 n₂ = 380 x₁ = 84 x₂ = 95

A poll checking on the level of public support for a tax increase reported that 19% of the respondents were in favour.The pollsters reported a sampling error of ±5%.When the responses were broken down by gender,support was 3% higher among women than men.The pollsters said the margin of error for this difference was ±6%.Why is the margin of error larger for the difference in support between the genders than for the overall level of support?

A survey of randomly chosen adults found that 30 of the 64 women and 49 of the 74 men follow regular exercise programs.Construct a 95% confidence interval for the difference in the proportions of women and men who have regular exercise programs.

Suppose that Statistics Canada wants to compare the current unemployment rate between Montreal and Toronto.Let And Represent the current unemployment rates in Montreal and the current A study found a 90% confidence interval for - Is (-0.0457,0.0424).Give an interpretation of this confidence interval.

A university wishes to compare the proportions of female students in the science and social science programs.A random sample of 120 science students contained 43 females.A random sample of 200 social science students contained 132 females.Construct a 99% confidence interval for the difference in the proportions of female students in the science and social science programs at this university.

A researcher wishes to determine whether the proportion of Canadian women who smoke differs from the proportion of Canadian men who smoke.He wants to test the hypothesis : = where represents the proportion of Canadian women who smoke and represents the proportion of Canadian men who smoke.He randomly selects 100 married couples.Among the 100 women in the sample are 21 smokers.Among the 100 men are 29 smokers.Are the assumptions for a two-sample z-test for two population proportions met? If not,which assumption is violated and why?