A small machine shop makes a part for Harley Davidson Motorcycles that needs to be 18.0 mm in diameter. The team that produces the part does a daily quality control check by randomly selecting n = 12 parts (using a systematic random sampling method). One day of operation the SRS produced a sample mean diameter of 17.96. Historically the machinery making the part has a population standard deviation of 0.09mm. We are investigating to see of the sample mean is significant at the 5% level.

What is the significance level for this test?

Question

A small machine shop makes a part for Harley Davidson Motorcycles that needs to be 18.0 mm in diameter. The team that produces the part does a daily quality control check by randomly selecting n = 12 parts (using a systematic random sampling method). One day of operation the SRS produced a sample mean diameter of 17.96. Historically the machinery making the part has a population standard deviation of 0.09mm. We are investigating to see of the sample mean is significant at the 5% level.

What is the significance level for this test?

BlackTom AI · Accepted Answer

The question asks for the significance level to use for this hypothesis test.

First, recall that the significance level, often denoted alpha (α), is the probability of committing a Type I error if the null hypothesis is true. It is a threshold chosen by the researcher before collecting or examining the data to determine how extreme the sample result must be to reject the null.

In this problem, the wording explicitly states that we are investigating to see if the sample mean is significant at the 5% level. This is a direct specification of α = 0.05.

Because the sample size is n = 12 and the population standard deviation is known (σ = 0.09 mm), this setup would typically use a z-test for the mean when applying the known-variance approach to determine whether the observed sample mean of 17.96 mm is significantly different from the target 18.0 mm, using α = 0.05.

If there were alternative choices, they would correspond to other common significance levels such as 0.01 or 0.10, but the problem clearly identifies 5% as the level to use.

Understanding this helps you set the critical z-value (approximately ±1.96 for a two-sided test at α = 0.05) and decide whether the observed sample mean falls into the rejection region for the null hypothesis that the population mean equals 18.0 mm.

In summary, the significance level is the pre-specified probability threshold for rejecting the null hypothesis, and the problem states this threshold as 5% (α = 0.05). Therefore, any inference from the sample will be made with that α in mind.

类似问题

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以下哪项不适合作为显著性水平的解释？

3. Level of significance (be careful as to one-tailed or two-tailed)

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