## Exercise \(\PageIndex{12}\).**15**.

A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, \(H_0\), is: the surgical procedure will go well. State the Type I and Type II errors in complete sentences.

16.

A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, \(H_0\), is: the surgical procedure will go well. Which is the error with the greater consequence?

17.

The power of a test is 0.981. What is the probability of a Type II error?

**18**.

A group of divers is exploring an old sunken ship. Suppose the null hypothesis, \(H_0\), is: the sunken ship does not contain buried treasure. State the Type I and Type II errors in complete sentences.

**19**.

A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis, \(H_0\), is: the sample does not contain E-coli. The probability that the sample does not contain E-coli, but the microbiologist thinks it does is 0.012. The probability that the sample does contain E-coli, but the microbiologist thinks it does not is 0.002. What is the power of this test?

**20**.

A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis, \(H_0\), is: the sample contains E-coli. Which is the error with the greater consequence?

## 9.3 Distribution Needed for Hypothesis Testing

21.

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

22.

Which distribution do you use when you are testing a population mean and the population standard deviation is known? Assume sample size is large. Assume a normal distribution with \(n \geq 30\).

**23**.

Which distribution do you use when the standard deviation is not known and you are testing one population mean? Assume a normal distribution, with \(n \geq 30\).

**24**.

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.

**25**.

A population has a mean is 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?

**26**.

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?

**27**.

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?

**28**.

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?

**29**.

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

**30**.

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?

**31**.

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

## 9.4 Full Hypothesis Test Examples

32.

Assume \(H_0: \mu = 9\) and \(H_a: \mu < 9\). Is this a left-tailed, right-tailed, or two-tailed test?

33.

Assume \(H_0: \mu \leq 6\) and \(H_a: \mu > 6). Is this a left-tailed, right-tailed, or two-tailed test?

**34**.

Assume \(H_0: p = 0.25\) and \(H_a: p \neq 0.25\). Is this a left-tailed, right-tailed, or two-tailed test?

**35**.

Draw the general graph of a left-tailed test.

**36**.

Draw the graph of a two-tailed test.

**37**.

A bottle of water is labeled as containing 16 fluid ounces of water. You believe it is less than that. What type of test would you use?

**38**.

Your friend claims that his mean golf score is 63. You want to show that it is higher than that. What type of test would you use?

**39**.

A bathroom scale claims to be able to identify correctly any weight within a pound. You think that it cannot be that accurate. What type of test would you use?

**40**.

You flip a coin and record whether it shows heads or tails. You know the probability of getting heads is 50%, but you think it is less for this particular coin. What type of test would you use?

**41**.

If the alternative hypothesis has a not equals ( \(\neq\) ) symbol, you know to use which type of test?

**42**.

Assume the null hypothesis states that the mean is at least 18. Is this a left-tailed, right-tailed, or two-tailed test?

**43**.

Assume the null hypothesis states that the mean is at most 12. Is this a left-tailed, right-tailed, or two-tailed test?

**44**.

Assume the null hypothesis states that the mean is equal to 88. The alternative hypothesis states that the mean is not equal to 88. Is this a left-tailed, right-tailed, or two-tailed test?