Hypothesis Testing Sample Exercises

  1. Which one of the following is NOT a step of performing a hypothesis test?

    A. construct the null and alternative hypothesis
    B. choose an appropriate significance level
    C. calculate the test statistic
    D. compare the test statistic with the significance level
    E. find the p-value of the test statistic

  2. In some mining operations, a byproduct of the processing is mildly radioactive. Of prime concern is the possibility that release of these byproducts into the environment may contaminate the freshwater supply. There are strict regulations for the maximum allowable radioactivity in supplies of drinking water, namely an average of 5 picocuries per litre (pCi/L) or less. However, it is well known that even safe water has occasional hot spots that eventually get diluted, so samples of water are assumed safe unless there is evidence to the contrary. A random sample of 25 specimens of water from a city's water supply gave a mean of 5.39 pCi/L and a standard deviation of 0.87 pCi/L. The appropriate null hypothesis is

    A.
    B.
    C.
    D.
    E.

  3. In the previous question, the appropriate alternative hypothesis is

    A.
    B.
    C.
    D.
    E.

  4. Which one of the following statements is NOT correct?

    A. the null hypothesis expresses the idea of some change, some difference or inequality
    B. the null hypothesis expresses the idea of no difference, no chance or equality
    C. the alternative hypothesis expresses the idea of some change, some difference or inequality
    D. the null and alternative hypotheses are mutually exclusive
    E. none of the above

  5. The profit per new car sold by an automobile dealer varies from car to car. The average profit per sale tabulated for the past 6 days was $368 with a standard deviation of $190. To test if there is sufficient evidence to indicate that average profit per sale is less than $480, the appropriate null hypothesis is

    A.
    B.
    C.
    D.
    E.

  6. In the previous question, the appropriate alternative hypothesis is:

    A.
    B.
    C.
    D.
    E.

  7. In question #5, the appropriate alternative hypothesis

    A. is one-sided
    B. is two-sided
    C. can be one-sided or two-sided
    D. hard to tell if it is one-sided
    E. none of the above

  8. Consider the following table in reference to the testing of a null hypothesis, which of the following is NOT correct?

    A. entry a corresponds to correct decisions
    B. entry c corresponds to incorrect decisions
    C. a Type I error occurs for entry c
    D. power refers to P(entry d)
    E. a Type II error occurs for entry a

  9. Let p = probability of Type I error, then 1- p is

    A. the probability of rejecting when is true
    B. the probability of not rejecting when is true
    C. the probability of not rejecting when is true
    D. the probability of rejecting when is true
    E. none of the above

  10. Which one of the following statements is NOT correct?

    A. the p-value measures the probability that the null hypothesis is true
    B. the level of significance is the probability of type I error
    C. in a statistical test of hypothesis, if the level of significance is reduced, the rejection region is reduced in size
    D. the null hypothesis will not be rejected unless the p-value indicates the data are very unusual assuming that the null hypothesis is true
    E. none of the above