Question

In​ 1996, 61​% 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 236 of 400 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 alphaequals0.10 level of​ significance, compute the probability of making a Type II​ error, beta​, if the true population proportion is 0.59. What is the power of the​ test? ​(c) Redo part​ (b) if the true population proportion is 0.56. ​(a) What does it mean to make a Type II error for this​ test? Choose the correct answer below. A. Upper H 0 is not rejected and the true proportion of high school teachers who believe that students are not attentive in the classroom is not equal to 0.61. B. Upper H 0 is not rejected and the true proportion of high school teachers who believe that students are not attentive in the classroom is equal to 0.61. C. Upper H 0 is rejected and the true proportion of high school teachers who believe that students are not attentive in the classroom is not equal to 0.61. ​(b) If the researcher decides to test this hypothesis at the alphaequals0.10 level of​ significance, compute the probability of making a Type II​ error, beta​, if the true population proportion is 0.59. What is the power of the​ test? beta equals nothing Power equals nothing ​(Type integers or decimals rounded to four decimal places as​ needed.) ​(c) Redo part​ (b) if the true population proportion is 0.56. beta equals nothing Power equals nothing ​(Type integers or decimals rounded to four decimal places as​ needed.)

Answer 1

Hypotheses are:

(a)

Type II error is the probability of fail to reject the false null hypothesis. That is teacher incoorectly conclude that proprotion is 0.61 while actually it is different than 0.61. Correct option is:

A. Upper H 0 is not rejected and the true proportion of high school teachers who believe that students are not attentive in the classroom is not equal to 0.61.

(b)

Answer: beta = 0.2135, power = 0.7865

(c)

Answer: beta = 0.6556, power = 0.3444