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Chapter 8: Q. 9.75 (page 380)

We have been provided a scenario for a hypothesis test for a population mean. Decide whether the z-test is an appropriate method for conducting the hypothesis test. Assume that the population standard deviation is known in the given case.

Preliminary data analyses reveal that the sample data contain no outliers but that the distribution of the variable under consideration is probably highly skewed. The sample size is70.

Short Answer

Expert verified

The use of the z-test is appropriate.

Step by step solution

01

Step 1. Given information.

Consider the given question,

The sample size is 70.

02

Step 2. Consider the given size.

Assume that the population standard deviation is known.

To decide whether the z-test can be used for conducting the hypothesis test or not, we need to take care of the following conditions,

In case the sample size isn<15, then the z-test procedure can be used when the variable is very close to being normally distributed or normally distributed.

If the sample size is between15<n<30, then the z-test procedure can be used when there is no outlier in the data or the variable is far from being normally distributed.

If the sample size is greater than 30<n, then the z-test procedure can be used without any limitation.

Here, the given sample size is large. This means, the sample size large.

The distribution of the variable under consideration is also mildly skewed and there is no outliers.

Therefore, the z-test is an appropriate method for conducting the hypothesis test as the data set is large.

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