# Distribution Needed for Hypothesis Testing (Exercises)

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Exercise \(\PageIndex{1}\)

Which two distributions can you use for hypothesis testing for this chapter?

**Answer**

A normal distribution or a Student’s *t*-distribution

Exercise \(\PageIndex{2}\)

Which distribution do you use when you are testing a population mean and the standard deviation is known? Assume sample size is large.

Exercise \(\PageIndex{3}\)

Which distribution do you use when the standard deviation is not known and you are testing one population mean? Assume sample size is large.

**Answer**

Use a Student’s \(t\)-distribution

Exercise \(\PageIndex{4}\)

A population mean is 13. The sample mean is 12.8, and the sample standard deviation is two. The sample size is 20. What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.

Exercise \(\PageIndex{5}\)

A population has a mean of 25 and a standard deviation of five. The sample mean is 24, and the sample size is 108. What distribution should you use to perform a hypothesis test?

**Answer**

a normal distribution for a single population mean

Exercise \(\PageIndex{6}\)

It is thought that 42% of respondents in a taste test would prefer Brand *A*. In a particular test of 100 people, 39% preferred Brand *A*. What distribution should you use to perform a hypothesis test?

Exercise \(\PageIndex{7}\)

You are performing a hypothesis test of a single population mean using a Student’s \(t\)-distribution. What must you assume about the distribution of the data?

**Answer**

It must be approximately normally distributed.

Exercise \(\PageIndex{8}\)

You are performing a hypothesis test of a single population mean using a Student’s \(t\)-distribution. The data are not from a simple random sample. Can you accurately perform the hypothesis test?

Exercise \(\PageIndex{9}\)

You are performing a hypothesis test of a single population proportion. What must be true about the quantities of \(np\) and \(nq\)?

**Answer**

They must both be greater than five.

Exercise \(\PageIndex{10}\)

You are performing a hypothesis test of a single population proportion. You find out that \(np\) is less than five. What must you do to be able to perform a valid hypothesis test?

Exercise \(\PageIndex{11}\)

You are performing a hypothesis test of a single population proportion. The data come from which distribution?

**Answer**

binomial distribution