The population mean of a certain population is thought to equal 140. Assume the

Question

The population mean of a certain population is thought to equal 140. Assume the value of the population standard deviation is 24. Repeated samples of size 36 were drawn from this population. Consider the set of sample means that result from this sampling situation to answer the questions in this assignment.

What is the mean of the resulting sample means in this situation, if the population mean really is equal to 140?

What is the standard deviation of the resulting sample means in this situation?

What is the alternative hypothesis if the research question is, “Do the data indicate that the mean exceeds 140?”

What is the value of the z test statistic associated with the sample mean of 148?

The test statistic must be greater than what value to reject the hypothesis that the population mean equals 140 and conclude that the mean exceeds 140 at the 5% significance level?

Explanation / Answer

a. mean of the resulting sample means = 140

b. standard deviation of the resulting sample means = 24/sqrt(36) = 24/6 = 4

c. Ha: mu > 140, H0: mu = 140

d. z-statistics = (148-140)/4 = 2

e. Critical value for 5% significance level = 1.645

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