Question

A technology company is studying the launch of their new laptop computers in order to track warranty purchases. The company states the average warranty length for their products is longer than 60 days.

If we would like to test the company's claim with a hypothesis test using a significance level of α=0.05 , which of the following choices are true?

Select the correct answer below:


There is a 5% chance we will conclude μ=60, but is in fact μ>60.

There is a 5% chance of rejecting the null hypothesis.

There is a 5% chance we will conclude μ>60, but is in fact μ=60.

There is a 5% chance that μ>60.

Answer 1

The correct statement for the hypothesis test at a 5% significance level is that there is a 5% chance we will conclude μ > 60 when, in fact, μ = 60, which is a Type I error.

Step-by-step explanation:

When a company claims their average warranty length for a new laptop is longer than 60 days, and we set up a hypothesis test with a significance level (alpha) of 0.05, we establish two hypotheses:

• Null hypothesis (H0): μ = 60 days

• Alternative hypothesis (Ha): μ > 60 days

This is a right-tailed test because we are testing if the mean (μ) is greater than a certain value. With α = 0.05, if we end up rejecting the null hypothesis, it means that there is sufficient evidence at the 5% level of significance to support the company's claim that the average warranty is greater than 60 days. However, stating 'there is a 5% chance that μ > 60' is incorrect because the significance level refers to the probability of making a Type I error, which is rejecting a true null hypothesis. Therefore, the correct statement would be:

• There is a 5% chance we will conclude μ > 60, but in fact μ = 60.

This statement refers to the risk of a Type I error where we incorrectly reject the null hypothesis when it is actually true.