Exam 21: Comparing Two Proportions

You wish to construct a 95% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.05,what sample size should we take from each group? Assume equal sample sizes.

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. -In City A,7420 people are unemployed in a random sample of 143000 people.In City B,7642 people are unemployed in a random sample of 142000 people.

You wish to construct a 90% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.05,what sample size should we take from each group? Assume equal sample sizes.

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 3 out of 50 first year university students surveyed did not have jobs,while 7 out of 50 second year university students did not have jobs during the academic year.

Use the given sample data to test the claim that p₁ > p₂.Use a significance level of 0.01.

A study investigated the smoking status of people in two age groups.Let Represent the proportion of people aged 20-24 who are smokers.Let Represent the proportion of people aged 25-29 who are smokers.A 95% confidence interval for the difference in smoking rates for - Was found to be (0.045,0.112).Give an interpretation of this confidence interval.

A study was conducted to determine if patients recovering from knee surgery should receive physical therapy two or three times per week.Suppose Represents the proportion of patients who showed improvement after one month of therapy three times a week and Represents the proportion of patients who showed improvement after one month of therapy twice a week.A 90% confidence interval for - Is (0.15,0.39).Give an interpretation of this confidence interval.

You wish to construct a 90% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.03,what sample size should we take from each group? Assume equal sample sizes.

You wish to construct a 95% 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.

A marketing survey involves product recognition in Ontario and British Columbia.Of 558 Ontario residents surveyed,193 knew the product while 196 out of 614 British Columbia residents knew the product.At the 0.05 significance level,do the data provide sufficient evidence to conclude that the recognition rate in Ontario differs from the recognition rate in British Columbia?

A researcher finds that of 1,000 people who said that they attend a religious service at least once a week,31 stopped to help a person with car trouble.Of 1,200 people interviewed who had not attended a religious service at least once a month,22 stopped to help a person with car trouble.At the 0.05 significance level,do the data provide sufficient evidence to conclude that the two proportions are different?

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 weight loss centre in the city provided a weight loss for 152 out of 200 participants.A weight loss centre in the suburb provided a weight loss for 109 out of 140 participants.

A poll of randomly selected Canadians between the ages of 20 and 29 reports that 35 of 410 men and 59 of 398 women suffered from insomnia at least once a week during the past year.

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 study investigated the smoking status of people in two age groups.A random sample of 100 people aged 20-24 revealed 24 who are smokers.A random sample of 120 people aged 25-29 revealed 15 who are smokers.

Suppose the proportion of first year students at a particular university who purchased used textbooks in the past year is and the proportion of second year students at the university who purchased used textbooks in the past year is .A study found a 95% confidence interval for - is (0.237,0.421).Does this interval suggest that first year students are more likely than second year students to buy used textbooks? Explain.

In a random sample of 500 people aged 20-24,22% were smokers.In a random sample of 450 people aged 25-29,14% were smokers.Do the data provide sufficient evidence to conclude that the proportion of smokers in the 20-24 age group is different from the proportion of smokers in the 25-29 age group? Use a significance level of 0.01.

Suppose the proportion of women who follow a regular exercise program is and the proportion of men who follow a regular exercise program is .A study found a 98% confidence interval for - is (-0.022,0.111).Does this study provide strong evidence of a gender-based difference in exercise? Explain.

Suppose the proportion of people losing weight at a city weight loss centre is And the proportion of people losing weight at a suburban weight loss centre is .A study found a 98% confidence interval for - Is (-0.1263,0.0891).Give an interpretation of this confidence interval.

The weight loss franchise home office wanted to compare the results of two centres.A centre in the city provided a weight loss for 152 out of 200 participants.A centre in the suburb provided a weight loss for 109 out of 140 participants.Construct a 98% confidence interval for the difference in the proportions of participants in the city weight loss centre and suburban weight loss centre.

Suppose that you perform a two-proportion z-test and reject the null hypothesis that there is no difference in the two proportions.If that conclusion is actually wrong,which type of error did you commit?