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

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) (Show Source): You can put this solution on YOUR website!
a)

b) Since this is considered small sampling (n < 30), we use the t-statistic.
. The critical value at the 0.025 significance level is . Since , 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.

RELATED QUESTIONS
The Admissions officer for the graduate programs at the University of Pennsylvania... (answered by robertb)

The Admissions officer for the graduate programs at the University of Pennsylvania... (answered by stanbon)

The director of admissions at Kinzua University in Nova Scotia estimated the distribution (answered by robertb)

At one prestigious university an SAT-Math score in the top 2% of the population is... (answered by ewatrrr)

The director of admissions at Kinzua University in Nova Scotia estimated the distribution (answered by Boreal)

Katherine D'Ann is planning to finance her college education by selling Programs at the... (answered by blairbear252)

Dear Dr. Professor, I would really appreaciate if you can help me with the following... (answered by stanbon)

Using data compiled by the Admissions Office at an imaginary university, college... (answered by stanbon,solver91311)

This is my last question need the solution stuck on it. How many different ways are... (answered by stanbon,Edwin McCravy)