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The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 5.00 minutes. To make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 33 randomly selected calls. The mean wait time was calculated to be 5.20 minutes. Assuming the population standard deviation is 0.57 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 5.00 minutes with a [tex]$99 \%$[/tex] level of confidence?

Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below.
[tex]\[
\begin{array}{l}
H_0: \mu = 5.00 \\
H_a: \mu \neq 5.00
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's start by clearly defining the null and alternative hypotheses for this hypothesis test.

- The null hypothesis (denoted as [tex]\( H_0 \)[/tex]) represents the status quo or a statement we aim to test. In this scenario, the null hypothesis is that the mean wait time is equal to 5.00 minutes.
- The alternative hypothesis (denoted as [tex]\( H_1 \)[/tex]) represents what we seek evidence for. Here, we want to determine if the mean wait time is greater than 5.00 minutes.

Hence, we can state the hypotheses as follows:

[tex]\[ \begin{array}{l} H_0: \mu = 5.00 \\ H_1: \mu > 5.00 \end{array} \][/tex]
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