Short Task 12

Complete at least 3 questions from this exam review (but do as much as you can and have questions prepared for the review session on Wednesday).

Exam 3 review

  1. Match the following phrases to items A-D. in the chart below appropriately (Note: if this question appears in the quiz there is no guarantee that it will appear in the same way).
  • Correct decision
  • Correct decision
  • Type I error
  • Type II error
\(H_0\) is true \(H_0\) is not true
\(H_0\) is rejected A. C.
\(H_0\) is not rejected B. D.

  1. Find the critical value(s) for the following situations. Assume that \(\sigma\) is known:

    1. \(H_A\): \(\bar x\) < \(\mu\), \(\alpha\) = 0.01, n = 15
    2. \(H_A\): \(\bar x\) \(\ne\) \(\mu\), \(\alpha\) = 0.05, n = 37
    3. \(H_A\): \(\bar x\) \(\ne\) \(\mu\), \(\alpha\) = 0.01, n = 12
    4. \(H_A\): \(\bar x\) > \(\mu\), \(\alpha\) = 0.01, n = 125
    5. \(H_A\): \(\bar x\) < \(\mu\), \(\alpha\) = 0.10, n = 5

  2. A researcher suspects that the number of tornadoes in northern Wisconsin significantly differs from other parts of the state and wants to test this hypothesis at \(\alpha = 0.01\). The mean for the entire state is 12 per decade. A sample of 10 counties in northern Wisconsin has a mean of 7 tornadoes per decade with a standard deviation of 3.6. For this problem, state:

    1. The null and alternative hypotheses
    2. The confidence level
    3. The test type (z or t) and reasoning for your choice
    4. Whether the test is one-tailed or two-tailed
    5. Critical value(s)
    6. Test statistic
    7. Decision

  3. A researcher suspects that the number of burial mounds in a group of counties in Georgia is significantly greater than other parts of the state and wants to test this hypothesis at \(\alpha = 0.05\). The mean for counties across the entire state is 27. A sample of 8 counties in the area of interest has a mean of 41 with a standard deviation of 9.2. For this problem, state:

    1. The null and alternative hypotheses
    2. The confidence level
    3. The test type (z or t) and reasoning for your choice
    4. Whether the test is one-tailed or two-tailed
    5. Critical value(s)
    6. Test statistic
    7. Decision

  4. Find the p-value based on the following scenarios and test statistics (2 points):

    1. \(H_A\): \(\bar x\) < \(\mu\), z = -1.07, n = 1152
    2. \(H_A\): \(\bar x\) > \(\mu\), t = 3.72, n = 27
    3. \(H_A\): \(\bar x\) > \(\mu\), t = -1.41, n = 18