SOLUTION: The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than t

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Question 1026067: The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1300. An accepted standard deviation for LSAT scores is 125. A random sample of 25 scores had an average of 1375.
a) State the appropriate null and alternative hypotheses.
b) Calculate the value of the test statistic and set up the rejection region at the 0.025 level. What is your conclusion?
c) Calculate the p-value.
Answer by robertb(5830) About Me  (Show Source):
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a) H%5B0%5D%3A+mu+=+1300
h%5Ba%5D%3A+mu+%3E+1300
b) Since this is considered small sampling (n < 30), we use the t-statistic.
. The critical value at the 0.025 significance level is t%5Bc%5D+=+2.064. Since t+=+3+%3E+t%5Bc%5D+=+2.064, the null hypothesis is rejected and conclude that the average score on the LSAT exam at UPenn is significantly higher than the national average.
c) The p-value for this t-statistic t = 3 with df = 24, is 0.003103 (Refer to https://www.easycalculation.com/statistics/p-value-t-test.php.)
Since the p-value of 0.003103 < 0.025, the null hypothesis is rejected and conclude that the average score on the LSAT exam at UPenn is significantly higher than the national average.