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?
oa. ( h_{0}:mu = 3.75 )
( h_{1}:mu>3.75 )
ob. ( h_{0}:mu = 3.75 )
( h_{1}:mu<3.75 )
oc. ( h_{0}:mu = 3.75 )
( h_{1}:mu
eq3.75 )
od. ( h_{0}:mu
eq3.75 )
( h_{1}:mu = 3.75 )

Explanation:

Step1: Understand the claim

The claim is that the population mean \(\mu = 3.75\). The null hypothesis \(H_0\) is the statement of equality. The alternative hypothesis \(H_1\) is the statement that we are trying to find evidence for.

Step2: Analyze each option

• Option A: \(H_0:\mu = 3.75\), \(H_1:\mu>3.75\) is a right - tailed test. But the claim is about equality, and we are not just testing if it is greater.
• Option B: \(H_0:\mu = 3.75\), \(H_1:\mu<3.75\) is a left - tailed test. But the claim is about equality, and we are not just testing if it is less.
• Option C: \(H_0:\mu = 3.75\), \(H_1:\mu

eq3.75\) is a two - tailed test. When we test the claim that the mean is equal to a value, the alternative is that it is not equal (covers both directions of deviation from the claimed mean).

• Option D: \(H_0:\mu

eq3.75\), \(H_1:\mu = 3.75\) is incorrect because the null hypothesis should be the statement of equality for a hypothesis test about a mean.

Answer:

C. \(H_0:\mu = 3.75\), \(H_1:\mu
eq3.75\)