To determine which distribution the researcher should use, let's analyze the situation:

1. Key Information Provided:

   • The sample size is 53 months (large sample, $n > 30$).
   • The population standard deviation is known.
   • The hypothesis involves testing the mean against a specified value.

2. Key Decision Factor:

   • If the population standard deviation is known, the appropriate distribution is the normal distribution for the test statistic.

Answer:

The researchers should use the normal distribution.

Reason:

The normal distribution is appropriate because:

• The sample size is large ($n > 30$), making the Central Limit Theorem applicable.
• The population standard deviation is available, so there is no need to estimate it using the sample standard deviation (which would require the Student-t distribution).

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Do you have any questions or want further details? Here are some follow-up questions:

1. What steps should the researcher take to set up the hypothesis test?
2. How is the test statistic calculated using the normal distribution?
3. What is the difference between the normal and Student-t distributions?
4. How does the population standard deviation influence the choice of test?
5. Can the researcher conduct the test with a smaller sample size if the standard deviation is still known?

Tip:

Always check whether the population standard deviation is known to determine the correct distribution for hypothesis testing!