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Suppose you are doing a test on a proportion with the hypotheses $H_0$: p = 0.4, $H_a$: p $\neq$ 0.4. In addition, you plan to use a sample of 50 values, and a significance level of $\alpha$ = 0.05.

Find $\beta(0.44)$, the probability of making a type II error given that the true population proportion is p = 0.44.

I found 0.26421< p< 0.53579 and -2.56< z<1.42 but it seems to be wrong. Could someone helps me please?

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$\beta$=Type-II error=$P(accept~H_0|H_0~is~false)$

$0.26421< p< 0.53579$ is 95% CI

Now, find the probability of when you accept p, if true p=0.44.

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