Question

Using TI-83 Only

Please Show Step By Step

1.We test the hypothesis H0 :μ=239 vs. H1 :μ>239 and did not reject H0 for α = 0.10. If μ actually equals to 111, did we make a Type I error, Type II error or correct decision regarding H1?

2.We test the hypothesis H0 :p=0.85 vs. H1 :p>0.85 and did not reject H0 for α=0.01. If we change α to 0.05, will we reject H0?

3.We test the hypothesis H0 :μ=799 vs. H1 : μ ≠ 799 and did not reject H0 for α=0.01. If we construct a 95% confidence interval for the same μ, will it include the number 799?

Answer 1

(A) We didn’t rejected the null hypothesis, this means we assumed that null hypothesis is true, but actually mean is 111, i.e. not more than 239. So, the decision is correct because mean is not greater than 239. Null hypothesis can only be rejected when mean is more than 239

(B) If null hypothesis is not rejected at 0.01 alpha level, then this means that the p value must be greater than 0.01 level.

If p value is greater than 0.01, but less than 0.05, then only we will reject the null hypothesis

if p value is greater than 0.01 as well as 0.05, then we will not reject the null hypothesis

(C) If null hypothesis is not rejected at 0.01 significance level, then this means that the null value or 799 must be included in the 99% confidence interval

we know that 99% confidence interval is wider than 95%, this means that all the value of 95% confidence interval must also be included within 99% confidence interval

therefore, we can say that 95% confidence interval will also include 799