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

a) one student is chosen from classroom a, then a student is chosen from classroom b.

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b. this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes. this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes. this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes. this makes them dependent events.

Answer from: Quest

step-by-step explanation:

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