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 2.50 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 31 randomly selected calls. the mean wait time was calculated to be 2.77 minutes. assuming the population standard deviation is 0.74 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 2.50 minutes with a 99% level of confidence? step 1 of 3 : state the null and alternative hypotheses for the test. fill in the blank below. h0hμ=2.50: μ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯2.50

Certainly! Here are the hypotheses in a multiple-choice format:
a. H₀ μ= 2.50
H_μ> 2.50
b. H₀ μ< 2.50
H_ μ< 2.50
c. H₀ μ < 2.50
H_μ > 2.50
d. H₀ μ > 2.50
H_μ= 2.50

Answer 1

The correct hypothesis for the scenario where we test if the mean wait time is longer than 2.50 minutes with a 99% confidence level would be: H0: μ = 2.50 and Ha: μ > 2.50. This is a right-tailed test.

Step-by-step explanation:

The null hypothesis (H0) and alternative hypothesis (Ha) for the test are crucial parts of any hypothesis testing. In this scenario, where we are looking to test if the mean wait time for customers is longer than 2.50 minutes, the null hypothesis should state that the mean wait time is equal to 2.50 minutes. The alternative hypothesis should suggest that the mean wait time is greater than 2.50 minutes. Thus, the correct hypotheses would be:

H0: μ = 2.50 (The mean wait time is 2.50 minutes)

Ha: μ > 2.50 (The mean wait time is greater than 2.50 minutes)

From the multiple-choice options provided, the correct selection would be:

a. H0: μ = 2.50
Ha: μ > 2.50

This is a right-tailed test since the alternative hypothesis is concerned with the mean being greater than a certain value. If the test statistic calculated from the sample data falls within the critical region at the 99% level of confidence, we would reject the null hypothesis, suggesting there is sufficient evidence that the mean wait time exceeds 2.50 minutes.