If you want to know the range of likely values for a sample mean given a particular population mean, you should conduct a z-test.

Name: If you want to know the range of likely values for a sample mean given a particular population mean, you should conduct a z-test.
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A z-test is used to determine if there is a significant difference between sample and population means, not to find the range of likely values for a sample mean. To find the range, you would construct a confidence interval.

If You Want to Know the Range of Likely Values