A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team's previously tepid offense historically managed.After a few months,the team owner looks at the data to test the coach's claim.He takes a sample of 36 of the team's games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points.Over the past 10 years,the team had averaged 99 points.What is(are)the appropriate critical value(s)to test the new coach's claim at the 1% significance level?
A) −2.438
B) −2.438 and 2.438
C) 2.326
D) 2.438

Question

Quizplus · Accepted Answer

Since we are testing a claim against a historical average, we can use a one-sample t-test. 
The null hypothesis is: the team's scoring average under the new coach is the same as the historical average, i.e., μ = 99. 
The alternative hypothesis is: the team's scoring average under the new coach is greater than the historical average, i.e., μ > 99. 
We are given a sample mean (x̄ = 101), sample size (n = 36), and sample standard deviation (s = 6). 
We can calculate the t-test statistic as: 
t = (x̄ - μ) / (s / √n) = (101 - 99) / (6 / √36) = 3 
Using a t-distribution with degrees of freedom (df) = n-1 = 35, we can find the critical t-value for a one-tailed test at the 1% significance level. 
Using a t-table or calculator, we find the critical t-value to be 2.438 (approx). 
Since our calculated t-value of 3 is greater than the critical t-value of 2.438, we reject the null hypothesis and conclude that the team's scoring average under the new coach is significantly higher than the historical average at the 1% significance level. 
The appropriate critical value for this test is D: 2.438.

A Newly Hired Basketball Coach Promised a High-Paced Attack That