LeRoy, a starting player for a major college basketball team, made only 40% of h
ID: 2953648 • Letter: L
Question
LeRoy, a starting player for a major college basketball team, made only 40% of his free throws last season. During the summer hs worked on developing a softer shot in the hope of improving his free-throw accuracy. In the first eight games of this season. LeRoy made 25 free throws- in 40 attempts. Let p be his probability of making each free throw he shoots this season You want to investigate whether LeRoy's work n the summer resulted n a higher probability of free-throw successes. State the null and alternative hypotheses What is beta LeRoy's sample proportion of successes? Calculate the test statstic for testing H0 against H2, and determine the P-value. Are the results significant at the alpha = 0.01 level? Explan briefly. State your conclusion in the context of the problem. Give a 90% confidence interval for LeRoy's free-throw success.Explanation / Answer
Given p=0.4, n=40, phat=25/40=0.625 (a) The test hypothesis is Ho: p0.4 (b)phat=25/40=0.625 (c) The test statistic is Z=(phat - p)/p*(1-p)/n = (0.625-0.4)/sqrt(0.4*(1-0.6)/40)=3.56 The p-value is P(Z>3.56)= 0.000185 (d) Yes, the result is signficant at =0.01 since p-value issmaller than 0.01. (e) Since the p-value is smaller than =0.01, we rejectHo. (f) Given =0.1, Z(0.05)=1.645 (check normal table) The 90% CI is phat±Z*p*(1-p)/n -->0.625 ± 1.645*sqrt(0.4*(1-0.4)/40) -->(0.4976, 0.7524)Related Questions
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