Exam 21: Comparing Two Proportions

A new manager,hired at a large warehouse,was told to reduce the employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.The manager later compares the sick leave rate prior to the program starting (65 out of 250 employees were sick)to the sick leave rate one month into the program (60 out of 253 employees were sick).Construct a 98% confidence interval for the difference in the proportions of sick employees prior to the program and one month into the program.

In a random sample of 300 Canadian women,68% watch CBC News.In a random sample of 200 Canadian men,56% watch CBC News.Construct a 98% confidence interval for the difference in the proportions of women and men who watch CBC News.

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.Construct a 99% confidence interval for the difference in the proportions of Ontario and British Columbia residents who knew the product.

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 (0.232,0.421).Give an interpretation of this confidence interval.

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. -n₁ = 50 n₂ = 75 X₁ = 20 x₂ = 15

A university found it retained 25 students out of 352 in 2009 and 26 students out of 334 in 2010.Construct a 90% confidence interval for the difference in the proportions of students retained in 2003 and 2004.

You wish to construct a 95% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.03,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 new manager started a program on employee sick leave.The manager later compares the sick leave rate prior to the program starting (65 out of 250 employees were sick)to the sick leave rate one month into the program (55 out of 253 employees were sick).

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 (-0.028,0.114).Give an interpretation of this confidence interval.

A new manager,hired at a large warehouse,was told to reduce the employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.Suppose the proportion of the employees sick prior to the new program is And the employees sick after the new program is .A study found a 98% confidence interval for - Is (-0.0668,0.1125).Give an interpretation of this confidence interval.

A survey of randomly selected university students found that 83 of the 110 first year students and 87 of the 120 second year students surveyed had purchased used textbooks in the past year.Construct a 98% confidence interval for the difference in the proportions of first and second year university students who purchased used textbooks.

In a random sample of 360 women,65% watched CBC News.In a random sample of 220 men,60% watched CBC News.Test the claim that the proportion of women who watch CBC News is higher than the proportion of men who watch CBC News.Use a significance level of 0.05.

7 of 8,500 people vaccinated against a certain disease later developed the disease.18 of 10,000 people vaccinated with a placebo later developed the disease.Test the claim that the vaccine is effective in lowering the incidence of the disease.Use a significance level of 0.02.

A university is studying the proportion of students retained in various years.Suppose the proportion of students retained in 2009 is And the proportion of students retained in 2010 is .A study found a 90% confidence interval for - Is (-0.0398,0.0262).Give an interpretation of this confidence interval.

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.Construct a 95% confidence interval for the difference in smoking rates for the two groups.

In Canada,a person with a body mass index (BMI)of 30 more is considered to be "obese." A random sample of 100 Canadian men revealed 26 to be obese.A random sample of 100 Canadian women revealed 21 to be obese.Construct a 90% confidence interval for the difference in the proportions of obese Canadian men and women.

A Member of Parliament wants to measure the level of support in his area for campaign finance reform and determine if there is a gender gap among voters with respect to this issue.One aide suggests that they find separate confidence intervals for the percent of men and the percent of women who favour reform and then see if the intervals overlap.Another aide suggests that they find a confidence interval for the difference in the proportions of men and women who favour reform.Which is the correct approach? Why?

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. -n₁ = 200 n₂ = 100 X₁ = 11 x₂ = 8

A researcher wished to test the claim that the rate of defectives among the computers of two different manufacturers is the same.She selected two independent random samples and found that 1.5% of 400 computers from manufacturer A were defective and 3.5% of 200 computers from manufacturer B were defective.

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 university found it retained 25 students out of 352 in 2009 and 36 students out of 334 in 2010.