Question 1

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?

Accepted Answer

The answer of Suppose that you perform a two-proportion z-test...

Question 2

A study investigated the smoking status of people in two age groups.Let $\mathrm { P } 1$ represent the proportion of people aged 20-24 who are smokers.Let $\mathrm { P } 2$ represent the proportion of people aged 25-29 who are smokers.A 95% confidence interval for the difference in smoking rates for $\mathrm { P } 1$ - $\mathrm { P } 2$ was found to be (0.045,0.112).Give an interpretation of this confidence interval.

Accepted Answer

A) We know that 95% of the proportion of smokers aged 25-29 is between 4.5% and 11.2% lower than the proportion of smokers aged 20-24. 
B) We know that 95% of all random samples done on the population will show that the proportion of smokers aged 20-24 is between 4.5% and 11.2% higher than the proportion of smokers aged 25-29. 
C) We are 95% confident that the proportion of smokers aged 25-29 is between 4.5% and 11.2% higher than the proportion of smokers aged 20-24. 
D) We know that 95% of the proportion of smokers aged 20-24 is between 4.5% and 11.2% more than the proportion of smokers aged 25-29. 
E) We are 95% confident that the proportion of smokers aged 20-24 is between 4.5% and 11.2% higher than the proportion of smokers aged 25-29.

Question 3

A university found it retained 25 students out of 352 in 2012 and 36 students out of 334 in 2013.

Accepted Answer

A) P-value = 0.0455; If there is no difference in the proportions,there is about a 4.55% chance of seeing the observed difference or larger by natural sampling variation. 
B) P-value = 0.9545; If there is no difference in the proportions,there is about a 95.45% chance of seeing the observed difference or larger by natural sampling variation. 
C) P-value = 0.0455; There is about a 4.55% chance that the two proportions are equal. 
D) P-value = 0.091; There is about a 9.1% chance that the two proportions are equal. 
E) P-value = 0.091; If there is no difference in the proportions,there is about a 9.1% chance of seeing the observed difference or larger by natural sampling variation.

Question 4

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 $p _ { p }$ and the employees sick after the new program is $\mathrm { Pa }$ .A study found a 98% confidence interval for $p _ { p }$ - $\mathrm { Pa }$ is (-0.0668,0.1125).Give an interpretation of this confidence interval.

Accepted Answer

A) We know that 98% of the employees sick after the new program is between 6.68% less and 11.25% more than the employees sick prior to the new program. 
B) We are 98% confident that the proportion of the employees sick prior to the new program is between 6.68% less and 11.25% more than the proportion of the employees sick after the new program. 
C) We know that 98% of all random samples done on the population will show that the proportion of the employees sick prior to the new program is between 6.68% less and 11.25% more than the proportion of the employees sick after the new program. 
D) We know that 98% of the employees sick prior to the new program is between 6.68% less and 11.25% more than the employees sick after the new program. 
E) We are 98% confident that the proportion of the employees sick after the new program is between 6.68% less and 11.25% more than the proportion of the employees sick prior to the new program.

Question 5

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.

Accepted Answer

A) (-0.44,-0.16) 
B) (-0.66,0.30) 
C) (-0.11,0.28) 
D) (-0.57,0.25) 
E) (0.30,0.66)

Question 6

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.

Accepted Answer

A) 1984 
B) 1201 
C) 601 
D) 1200 
E) 600

Question 7

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 p2.A study found a 95% confidence interval for p1 - p2 is $( 0.232,0.421 )$ Give an interpretation of this confidence interval.

Accepted Answer

A) We are 95% confident that at this university the proportion of second year students who bought used textbooks is between 23.2% and 42.1% higher than the proportion of first year students who bought used textbooks. 
B) We are 95% confident that at this university the proportion of first year students who bought used textbooks is between 23.2% and 42.1% higher than the proportion of second year students who bought used textbooks. 
C) We know that 95% of first year students bought between 23.2% and 42.1% more used textbooks than second year students at this university. 
D) We are 95% confident that first year students at this university bought between 23.2% and 42.1% more used textbooks than second year students. 
E) We know that 95% of all random samples done on the population will show that the proportion of first year students who bought used textbooks is between 23.2% and 42.1% higher than the proportion of second year students who bought used textbooks.

Question 8

A university found it retained 25 students out of 352 in 2012 and 26 students out of 334 in 2013.Construct a 90% confidence interval for the difference in the proportions of students retained in 2012 and 2013.

Accepted Answer

A) (-0.0461,0.0325) 
B) (-0.0535,0.0398) 
C) (-0.0585,0.0449) 
D) (-0.0398,0.0262) 
E) (0.0262,0.0398)

Question 9

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.

Accepted Answer

A) (0.017,0.234) 
B) (0.033,0.207) 
C) (0.017,0.223) 
D) (0.029,0.211) 
E) (0.006,0.234)

Question 10

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?

Accepted Answer

The answer of A marketing survey involves product recognition in...

Question 11

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?

Accepted Answer

The answer of A Member of Parliament wants to measure...

Question 12

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?

Accepted Answer

The answer of A researcher finds that of 1,000 people...

Question 13

Use the given sample data to test the claim that p1 > p2.Use a significance level of 0.01. $\begin{array} { ll } 
\underline{Sample 1} & \underline{Sample 2}\
\mathrm{n}_{1}=85 & \mathrm{n}_{2}=90\
x _ { 1 } = 38 & x _ { 2 } = 23 \
\end{array}$

Accepted Answer

The answer of Use the given sample data to test...

Exam 19: Comparing Two Proportions

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?

A university found it retained 25 students out of 352 in 2012 and 36 students out of 334 in 2013.

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 university found it retained 25 students out of 352 in 2012 and 26 students out of 334 in 2013.Construct a 90% confidence interval for the difference in the proportions of students retained in 2012 and 2013.

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.

Use the given sample data to test the claim that p1 > p2.Use a significance level of 0.01. $\begin{array} { ll } \underline{Sample 1} & \underline{Sample 2}\\\mathrm{n}_{1}=85 & \mathrm{n}_{2}=90\\x _ { 1 } = 38 & x _ { 2 } = 23 \\\end{array}$