ALL SOLUTIONS SHOULD BE ROUNDED TO THE FOURTH DECIM 14. (20 points) Susan, a sta

Question

ALL SOLUTIONS SHOULD BE ROUNDED TO THE FOURTH DECIM 14. (20 points) Susan, a starting playe AL (where applicable) r for the basketball team, made only 48% of her free throws last season. During e summer she worked on developing a softer shot in the hope of improving her free-throw accuracy. In the ftirst pan of the season, Susan made 31 free throws in 50 attempts. Do the data provide evidence that the summer wor improved her shot? f. Calculate the 95% confidence interval. g. Interpret the confidence interval How large a sample n would you need to estimate p with margin of error 0.05 with 90% confidence? conservative guess forp h. Use the most

Explanation / Answer

Solutionf:

p^=sample proportion=x/n=31/50

=0.62

z crti for 95%=1.96

95% confidence interval for popualtion mean is

p^-zsqrt(p^(1-p^/n),p^+zsqrt(p^(1-p^/n)

0.62-1.96*sqrt(0.62(1-0.62)/50), 0.62+1.96*sqrt(0.62(1-0.62)/50)

0.4855,0.7545

0.4855<p<0.7545

we are 95% confident that the true popualtion proportion of free throws lies in between

0.4855 and 0.7545

Solutionc:

p=1/2=0.5

z alpha/2 dor 90%=1.645

n=sample size

=Z^2 *p*(1-p)/E^2

=1.645^2*0.5(1-0.5)/0.05^2

= 270.6025

=271

required sample size=271

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