Quiz 3 in-class review session

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

    1. \(H_A\): \(\bar x\) \(\ne\) \(\mu\), \(\alpha\) = 0.01, n = 4
    2. \(H_A\): \(\bar x\) > \(\mu\), \(\alpha\) = 0.05, n = 37

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

    1. \(H_A\): \(\bar x\) < \(\mu\), z = 2.87, n = 1152
    2. \(H_A\): \(\bar x\) > \(\mu\), t = 3.72, n = 144

  3. A researcher suspects that the number of burial mounds in a group of counties in Montana is significantly different than other parts of the state and wants to test this hypothesis at \(\alpha = 0.01\). The mean for counties across the entire state is 101. A sample of 26 counties in the area of interest has a mean of 93 with a standard deviation of 12.5. 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. What is the relationship between critical values of z and critical values of t?

  5. When making a statistical decision based on a critical value and a test statistic, what are a researcher options? What should the researcher refrain from doing?

  6. A researcher conducts a study with a small sample size and fails to reject the null hypothesis. Later, after collecting more data, different researchers conduct a study with the same question and a large sample size, finding that the null hypothesis should be rejected. The first researcher committed what type of error?

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

    1. \(H_A\): \(\bar x\) < \(\mu\), \(\alpha\) = 0.01, n = 500
    2. \(H_A\): \(\bar x\) \(\ne\) \(\mu\), \(\alpha\) = 0.05, n = 25

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

    1. \(H_A\): \(\bar x\) < \(\mu\), t = 1.72, n = 27
    2. \(H_A\): \(\bar x\) > \(\mu\), z = -0.87, n = 307

  9. We are tasked with conducting a study on the amount of cadmium in local streams, and we are specifically concerned that Eau Claire County has significantly greater amounts than the state average. In the county we sample 32 streams and find a mean of 0.006 mg/L. The mean for the entire state is 0.003 mg/L with a standard deviation of 0.053. For this problem state:

    1. The null and alternative hypotheses
    2. An appropriate alpha
    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