3. (1 point) You know that the expected value of height is 6 feet, i.e. E(height

Question

3. (1 point) You know that the expected value of height is 6 feet, i.e. E(height) h -6. You decide to run an experiment to test one of the concepts you learned in your econometrics class. You take a random sample of 100 individuals, compute the sample average of their height (Ah) and test H0 : -6 with a significance level of 5 percent. You draw another random sample, compute (Ah) and test the same hypothesis with the same significance level. You do this 100 times. How many times, approximately, would you reject the null hypothesis?

Explanation / Answer

The Null hypothesis proposes that the mean height is 6 feet.

A significance level of 5% implies that values falling in the region of 2.5% on each side of the normal curve would be rejected.

Region of accetpance is given by the confidence interval with 95% confidence.

Probability that the sample mean lies in the confidence interval of 95% area = 0.95 and the probability that the sample mean lies outside the confidence limit = 0.05

So if the survey is repeated 100 times, the approximate number of rejections = 100 x 0.05 = 5

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