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Statistics LibreTexts

9.9: Chapter Practice

  • Page ID
    6095
  • 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?