Exam 19: Comparing Two Proportions

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 0.05,what sample size should we take from each group? Assume equal sample sizes.

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.

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.

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.

n1 = 200 n2 = 100 X1 = 11 x2 = 8

Suppose the proportion of women who follow a regular exercise program is $\mathrm { P } _ { \mathrm { W } }$ and the proportion of men who follow a regular exercise program is $\mathrm { Pm }$ .A study found a 98% confidence interval for $p _ { w } - p _ { m }$ is ( $- 0.028,0.114 )$ . Give an interpretation of this confidence interval.

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.

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.

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.

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.

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.

Suppose the proportion of first year students at a particular university who purchased used textbooks in the past year is $\mathrm { P } 1$ and the proportion of second year students at the university who purchased used textbooks in the past year is $\mathrm { P } 2$ .A study found a 95% confidence interval for $p _ { 1 } - p _ { 2 }$ 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.

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.

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 $\mathrm { H } _ { 0 } : \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ where $\mathrm { p } _ { 1 }$ represents the proportion of Canadian women who smoke and $\mathrm { P } _ { 2 }$ 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?

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 study was conducted to determine if patients recovering from knee surgery should receive physical therapy two or three times per week.Suppose $\text { P3 }$ represents the proportion of patients who showed improvement after one month of therapy three times a week and $\mathrm { P } 2$ represents the proportion of patients who showed improvement after one month of therapy twice a week.A 90% confidence interval for $\text { p3 - p2 }$ is $( 0.15,0.39 )$ 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 the proportion of people losing weight at a city weight loss centre is $\mathrm { P } _ { \mathrm { C } }$ and the proportion of people losing weight at a suburban weight loss centre is $p _ { s }$ .A study found a 98% confidence interval for $\mathrm { P } _ { \mathrm { C } }$ - $p _ { s }$ is (-0.1263,0.0891).Give an interpretation of this confidence interval.