Question

suppose you are running a hypothesis test for a population mean with the following settings.

• H 0 : μ ≤ 50H 0 : μ ≤ 50 and H 1 : μ > 50H 1 : μ > 50
• α = 0.05α = 0.05
• Which of the following values (45, 49, 51, or 55) is most likely to result in the outcome of “Reject the null hypothesis”? Explain.
• Describe how to determine the outcome of a hypothesis test using the P-value. (No specific values are needed here, just a general idea of how the process goes.)
• Describe how to determine the outcome of a hypothesis test using the rejection region. (No specific values are needed here, just a general idea of how the process goes.)
• Assume that, in fact, the population mean is equal to 50 (μμ = 50). If the result of the hypothesis test is to “Reject the null hypothesis”, then an error has just occurred.
  1. Explain why this is an error.
  2. What specific type of error is it (Type 1 or Type 2)?
  3. How often will a hypothesis test with the settings above result in this kind of error? Explain. PLEASE HELP ME WITH CLEAR ANSWERS I'M VERY CONFUSED

Answer 1

a. Since H₁: μ > 50, we accept that value>50 is likely to result in the outcome of reject the null hypothesis. Since 55 is maximum value of the given set of observations, most likely value that result in the outcome of “Reject the null hypothesis”=55.

b. Since sample mean is point estimator of population mean μ, the large value of is likely to result in the outcome of reject the null hypothesis.

Here we need to assume that sample come from normal population independently. Here population variance is known or unknown.

Case I: is known.

Case II:   is unknown

c.

Case I: is known.

Case II:   is unknown

d. The result of the hypothesis test is to “Reject the null hypothesis” but in reality it may not be true. Hence Type I error is committed.

P(Type I error) is less than equal to level of significance