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.
(round to two decimal places as needed.)

Explanation:

Step1: Calculate the test statistic

The formula for the \(t\) - test statistic in a one - sample \(t\) - test (since the population standard deviation \(\sigma\) is unknown) is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\).

We are given that \(n = 94\), \(\bar{x}=3.59\), \(s = 0.66\), and \(\mu = 3.75\).

Substitute the values into the formula:

$$
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$$

Step2: Simplify the expression

$$t\approx - 2.35$$

Answer:

The test statistic is approximately \(-2.35\)