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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
alpha=0.05, which of the following choices are true?
Select the correct answer below:
There is a
5% chance we will conclude
mu=60, but is in fact
mu > 60.
There is a
5% chance of rejecting the null hypothesis.
There is a
5% chance we will conclude
mu > 60, but is in fact
mu=60.
There is a
5% chance that
mu > 60.

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. $\newline$ If we would like to test the company's claim with a hypothesis test using a significance level of $\alpha=0.05$ , which of the following choices are true? $\newline$ Select the correct answer below: $\newline$ There is a $5 \%$ chance we will conclude $\mu=60$ , but is in fact $\mu>60$ . $\newline$ There is a $5 \%$ chance of rejecting the null hypothesis. $\newline$ There is a $5 \%$ chance we will conclude $\mu>60$ , but is in fact $\mu=60$ . $\newline$ There is a $5 \%$ chance that $\mu>60$ .

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Find probabilities using the addition rule

Full solution

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.

\newline

If we would like to test the company's claim with a hypothesis test using a significance level of

\alpha=0.05

, which of the following choices are true?

\newline

Select the correct answer below:

\newline

There is a

5 \%

chance we will conclude

\mu=60

, but is in fact

\mu>60

.

\newline

There is a

5 \%

chance of rejecting the null hypothesis.

\newline

There is a

5 \%

chance we will conclude

\mu>60

, but is in fact

\mu=60

.

\newline

There is a

5 \%

chance that

\mu>60

.

Significance Level Definition: The significance level, denoted as alpha ( $\alpha$ ), is the probability of rejecting the null hypothesis when it is actually true. This is also known as the Type I error rate. In this context, the null hypothesis ( $H_0$ ) is that the average warranty length ( $\mu$ ) is $60$ days, and the alternative hypothesis ( $H_1$ ) is that the average warranty length is greater than $60$ days ( $\mu > 60$ ).
Interpretation of Significance Level: Given that the significance level is $0.05$ , this means that there is a $5\%$ chance of making a Type I error, which is rejecting the null hypothesis when it is true. Therefore, the correct interpretation is that there is a $5\%$ chance we will conclude that the average warranty length is greater than $60$ days when in fact it is equal to $60$ days.
Correct Answer Explanation: The correct answer to the question is: ＂There is a $5\%$ chance we will conclude $\mu > 60$ , but is in fact $\mu=60$ .＂ This statement correctly describes the risk of a Type I error associated with a significance level of $0.05$ .

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\newline

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\newline

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