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9.3E: 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

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