Question

The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 4.00

minutes. To make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 59
randomly selected calls. The mean wait time was calculated to be 4.33
minutes. Assuming the population standard deviation is 1.42
minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 4.00
minutes with a 98%
level of confidence?
Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below.

H0Ha: μ=4.00: μ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯4.00

Answer 1

The null hypothesis (
`\(H_0\)`) asserts that the population mean wait time for customer service is at most 4.00 minutes. The alternative hypothesis (
`H_a\)`) contends that the mean wait time is longer than 4.00 minutes. This sets the stage for hypothesis testing.

The null and alternative hypotheses for the test can be stated as follows:

`\[ H_0: \mu \leq 4.00 \]`

`\[ H_a: \mu > 4.00 \]`

Where:

-
`\( H_0 \)` is the null hypothesis, representing the claim that the mean wait time is at most 4.00 minutes.

-
`\( H_a \)` is the alternative hypothesis, representing the assertion that the mean wait time is longer than 4.00 minutes.

So, in statistical terms, the null hypothesis (
`\( H_0 \)`) is that the population mean (
`\( \mu \)`) is less than or equal to 4.00 minutes, and the alternative hypothesis (
`\( H_a \)`) is that the population mean is greater than 4.00 minutes.