Mathematics, 19.01.2021 22:10 hbantzstudent

A survey found that 31 of 60 randomly selected women and 38 of 73 randomly selected men follow a regular exercise program. Find a 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program.

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Answer from: NehemiahPate2006

95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program

(-0.1740 , 0.1672)

Step-by-step explanation:

Step(i):-

Given A survey found that 31 of 60 randomly selected women

First sample proportion

$p_{1} = \frac{x_{1} }{n_{1} } = \frac{31}{60} = 0.5166$

Second sample proportion

$p_{2} = \frac{x_{2} }{n_{2} } = \frac{38}{73} = 0.520$

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step(ii):-

95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program

$((p_{1} ^{-}-p^{-} _{2} - Z_{0.05} S.E(p_{1} ^{-} - p^{-} _{2} ), (p_{1} ^{-}-p^{-} _{2} +Z_{0.05} S.E(p_{1} ^{-} - p^{-} _{2} ))$

where

$Se(p_{1} - p_{2} ) = \sqrt{\frac{p_{1} (1-p_{1} )}{n_{1} }+\frac{p_{2}(1-p_{2} }{n_{2} } }$

$Se(p_{1} - p_{2} ) = \sqrt{\frac{0.5166 (1-0.5166 )}{60 }+\frac{0.520(1-0.520 }{73 } } = 0.08706$

95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program

$((p_{1} ^{-}-p^{-} _{2} - Z_{0.05} S.E(p_{1} ^{-} - p^{-} _{2} ), (p_{1} ^{-}-p^{-} _{2} +Z_{0.05} S.E(p_{1} ^{-} - p^{-} _{2} ))$

((0.5166-0.520-1.96(0.08706) , 0.5166-0.520+1.96(0.08706))

(-0.1740 , 0.1672)

Final -

95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program

(-0.1740 , 0.1672)

Answer from: Quest

10cm

step-by-step explanation:

Answer from: Quest

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if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.

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