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In order to test ?0:?=.5 vs. ??:?<.5 using the .10 level of significance, a sample of...

In order to test ?0:?=.5 vs. ??:?<.5 using the .10 level of significance, a sample of ?=100 will be selected. Suppose that, in reality, the population proportion is .4.

(a) The probability the test will commit a type II error is   .___

(b) The power of the test is ___ .

Independent random samples, each containing 50 observations, were selected from two populations. The samples from populations 1 and 2 produced 30 and 25 successes, respectively.
Test ?0:(?1−?2)=0 against ??:(?1−?2)≠0. Use ?=0.05.

(a) The test statistic is  

(b) The P-value is

(c) The final conclusion is
A. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=0
B. We can reject the null hypothesis that (?1−?2)=0 and conclude that (?1−?2)≠0

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orchestra answered 1 year ago
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