A company claims that their average customer satisfaction score is 85. A sample of 30 customers is taken, and their average score is 82 with a standard deviation of 3. The alternative hypothesis is that the average customer satisfaction score is not 85. What type of test should be used?
Solution
Step 1 ：First, we identify the null and alternative hypotheses. The null hypothesis (H0) is that the average customer satisfaction score is 85, that is, H0: \(\mu = 85\). The alternative hypothesis (H1) is that the average customer satisfaction score is not 85, that is, H1: \(\mu \neq 85\).
Step 2 ：Second, we determine the type of test. The alternative hypothesis does not specify whether the true population mean is greater than or less than 85, it simply states that it is not equal to 85. This means that we are not concerned with one specific direction (greater than or less than).
Step 3 ：Hence, we need to use a two-tailed test. In a two-tailed test, the rejection region for a significance level \(\alpha\) is divided equally between the two tails of the distribution.
