ALL SOLUTIONS SHOULD BE ROUNDED TO THE FOURTH DECIMAL (where app 14. (20 points)

Question

ALL SOLUTIONS SHOULD BE ROUNDED TO THE FOURTH DECIMAL (where app 14. (20 points) Susan, a starti licable) ng player for the basketball team, made only 48% of her free throws last season. During summer she worked on developing a softer shot in the hope of improving her free-throw accuracy. In the first park of the season, Susan made 31 free throws in 50 attempts. Do the data provide evidence that the summer improved her shot? a. Check the needed conditions for both the test tatistic and confidence interval. (Do not do a stemplot.) b. State Ho and Ha c. Calculate the test statistic (if applicable- state the degrees of freedom) d. Find the p-value e. What is the conclusion for this problem? Do you reject Ho? f. Calculate the 95% confidence interval. g. Interpret the confidence interval large a sample" would you need to estimate p with margin of error 0.05 with 90% confidence? Use the most conservative guess for p.

Explanation / Answer

a) p =48% = 0.48

n= 50

x= 31

p^ =x/n= 31/50 = 0.62

b) under this test the null and alternative hypotheses are

Ho:p=0.48 ( there is no chnge in free throw probability)

Ha:p>0.48 (there is a significant improvement in the free throw probability )

c) to test the null hypothesis we have test statstics as

z= p^-p /sqrt(pq/n) = 0.62-0.48 / sqrt(0.48*0.52/31)=1.560

d) the corresponding p value is caluclated as

P(Z>1.560) =1-0.9406 =0.0594

e) since the caluclated p value is greater than the given level of significance we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim

according to chegg guidelines only 1st 4 to be answered for remaining ask in separate ques

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