Question $\newline$ 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 $\alpha=0.05$ , what is the rejection region? $\newline$ Use the graph below to show the rejection region. First, move the blue dot to choose the appropriate test (left-, right, or twotailed). Then, slide the shaded region(s) to represent the rejection region. $\newline$ Provide your answer below: $\newline$ Move the blue dot to choose the appropriate test

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Q. Question

\newline

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

\alpha=0.05

, what is the rejection region?

\newline

Use the graph below to show the rejection region. First, move the blue dot to choose the appropriate test (left-, right, or twotailed). Then, slide the shaded region(s) to represent the rejection region.

\newline

Provide your answer below:

\newline

Move the blue dot to choose the appropriate test

Question Prompt: The question prompt is: ＂What is the rejection region for a hypothesis test of a company's claim that the average warranty length for their products is longer than $60$ days, using a significance level of $\alpha=0.05$ ?＂
Type of Test: Since the company claims that the average warranty length is longer than $60$ days, we are dealing with a one-sided test where we are looking for evidence that the mean is greater than a certain value. This is a right-tailed test because we are testing if the mean is greater than $60$ days.
Rejection Region Location: In a right-tailed test, the rejection region is located in the right tail of the distribution. The significance level $\alpha=0.05$ tells us that the rejection region will contain the top $5\%$ of the probability distribution.
Find Critical Value: To find the rejection region for the right-tailed test, we need to determine the critical value that corresponds to the top $5\%$ of the standard normal distribution. This is typically found using a Z-table or statistical software. For a standard normal distribution, the critical value for $\alpha=0.05$ is approximately $1.645$ .
Rejection Region Determination: The rejection region for this hypothesis test is therefore all values to the right of the critical value of $1.645$ on the standard normal distribution curve. This means that if our test statistic is greater than $1.645$ , we would reject the null hypothesis in favor of the alternative hypothesis that the average warranty length is longer than $60$ days.