In 1996, 59 % of high school teachers felt it was a serious problem that high sc

Question

In 1996, 59 % of high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. A recent survey found that 285 of 500 high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. Do high school teachers feel differently today than they did in 1996?

(a) What does it mean to make a Type II error for this test?

(b) If the researcher decides to test this hypothesis at the alphaequals=0.10 level of significance, compute the probability of making a Type II error, beta , if the true population proportion is 0.57 What is the power of the test?

(c) Redo part (b) if the true population proportion is 0.54

Explanation / Answer

a) Type II error is failing to reject 0.59 even if it was wrong.

b) The mean is 0.59, sample size is 500. Hence the standard deviation of the sample proportions is square root of p into (1-p)/ sample size. Hence square root of 0.59 into 0.41/ 500 is coming to 0.021995. Hence, the 90% confidence interval is 0.553927 and 0.626073. The probability of Type II error is 0.762128. Power of the test is 1 minus Probability of Type II error, that is 1 - 0.762128 = 0.237872.

c) The mean is 0.59, sample size is 500. Hence the standard deviation of the sample proportions is square root of p into (1-p)/ sample size. Hence square root of 0.59 into 0.41/ 500 is coming to 0.021995. Hence, the 90% confidence interval is 0.736697 and 0.999954. The probability of Type II error is 0.263257. Power of the test is 1 minus Probability of Type II error, that is 1 - 0.263257 = 0.736743

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