Question

a data set includes data from student evaluations of courses. the summary statistics are ( n = 94 ), ( overline{x}=3.59 ), ( s = 0.66 ). use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 3.75. assume that a simple random sample has been selected. identify the null and alternative hypotheses, test statistic, p - value, and state the final conclusion that addresses the original claim.
what are the null and alternative hypotheses?
a. ( h_0:mu = 3.75 )( h_1:mu>3.75 )
b. ( h_0:mu = 3.75 )( h_1:mu<3.75 )
c. ( h_0:mu = 3.75 )( h_1:mu
eq3.75 )
d. ( h_0:mu
eq3.75 )( h_1:mu = 3.75 )
determine the test statistic.

• 2.35 (round to two decimal places as needed.)

determine the ( p ) - value.
0.020 (round to three decimal places as needed.)
state the final conclusion that addresses the original claim.
( h_0 ) there is evidence to conclude that the mean of the population of student course evaluations is equal to 3.75 correct.
fail to reject
reject

Explanation:

Step1: Hypothesis testing rule

If \(P - value\leqslant\alpha\), reject \(H_0\). Here \(\alpha = 0.10\), and \(P - value=0.020\).

Step2: Conclusion

Since \(0.020<0.10\), we reject \(H_0\).

Answer:

Reject \(H_0\). There is sufficient evidence to conclude that the mean of the population of student course evaluations is not equal to \(3.75\) (the original claim that \(\mu = 3.75\) is rejected).