Suppose the proportion of women who follow a regular exercise program is $p _ { w }$ and the proportion of men who follow a regular exercise program is $p _ { m }$. A study found a $98 \%$ confidence interval for $p _ { w } - p _ { m }$ is $( - 0.024,0.115 )$. Give an interpretation of this confidence interval.

A) We are $98 \%$ confident that the proportion of women who follow a regular exercise program is between $2.4 \%$ less and $11.5 \%$ more than the proportion of men who follow a regular exercise program.

B) We are $98 \%$ confident that the proportion of men who follow a regular exercise program is between $2.4 \%$ less and $11.5 \%$ more than the proportion of women who follow a regular exercise program.

C) We know that $98 \%$ of men exercise between $2.4 \%$ less and $11.5 \%$ more than women.

D) We know that $98 \%$ of all random samples done on the population will show that the proportion of women who follow a regular exercise program is between $2.4 \%$ less and $11.5 \%$ more than the proportion of men who follow a regular exercise program.

E) We know that $98 \%$ of women exercise between $2.4 \%$ less and $11.5 \%$ more than men.

Question

Suppose the proportion of women who follow a regular exercise program is

p _ { w }

and the proportion of men who follow a regular exercise program is

p _ { m }

. A study found a

98 \%

confidence interval for

p _ { w } - p _ { m }

is

( - 0.024,0.115 )

. Give an interpretation of this confidence interval.

A) We are $98 \%$ confident that the proportion of women who follow a regular exercise program is between $2.4 \%$ less and $11.5 \%$ more than the proportion of men who follow a regular exercise program.

B) We are $98 \%$ confident that the proportion of men who follow a regular exercise program is between $2.4 \%$ less and $11.5 \%$ more than the proportion of women who follow a regular exercise program.

C) We know that $98 \%$ of men exercise between $2.4 \%$ less and $11.5 \%$ more than women.

D) We know that $98 \%$ of all random samples done on the population will show that the proportion of women who follow a regular exercise program is between $2.4 \%$ less and $11.5 \%$ more than the proportion of men who follow a regular exercise program.

E) We know that $98 \%$ of women exercise between $2.4 \%$ less and $11.5 \%$ more than men.

Quizplus · Accepted Answer

The confidence interval for $p _ { w } - p _ { m }$ from $-0.024$ to $0.115$ suggests that we are $98\%$ confident that the true difference in proportions (women minus men) falls within this range, meaning the proportion of women who follow a regular exercise program could be up to $2.4\%$ less than or up to $11.5\%$ more than the proportion of men who do so.

Suppose the Proportion of Women Who Follow a Regular Exercise pwp _ { w }pw​

Suppose the Proportion of Women Who Follow a Regular Exercise $p _ { w }$