1. In example ( A basketball player claims to be able to make over 80% of her fr

Question

1. In example ( A basketball player claims to be able to make over 80% of her free-throws. If she shoots 60 and makes 53, does this support her claim at the 1% significance level? Find the p-value.), we couldn’t prove the player made over 80% of all of her free throws at the 1% significance level even though she made 53 out of 60 (which is 88.3%).

(a) If she made 88.3% of the 50 free throws, why can’t we show that she makes over 80%?

(b) How many of the 60 would she have to make so that we could prove that she makes over 80% at the 1% significance level. Derive your answer mathematically (not by trial and errow) and show all of your work.

(c) At what significance level would 53 out of 60 allowed us to prove she can make over 80%? Show how you obtained your answer.

Explanation / Answer

Standard deviation. = sqrt[ P * ( 1 - P ) / n ], where P is the hypothesized value of population proportion in the null hypothesis
= 0.0516398

Test statistic.z = (p - P) / = (53/60 - 0.8)/0.0516398 = 1.6137
p for right tailed test = 0.053296

a) The significance level is very low and the p value is greater than the significance value, therefore we cannot show that she makes over 80% statistically(no sufficient evidence)

b) zcrit = 2.33 for 1% significance level
Test statistic.z = (p - P) / = (x/60 - 0.8)/0.0516398 = 2.33, x = 55.22 = 56 free throws

c) p for right tailed test = 0.053296, Any significance level equal to or over 5.4%

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