Question

Suppose you reject the null hypothesis H₀: μ = 58. It turns out the population mean is actually equal to 55.   You have made

A. Type I and Type II errors

B. the correct decision

C. a Type I error

D. a Type II error

We have created a 97% confidence interval for μ with the result [57, 97]. If we test H₀: μ=98 versus H₁: μ≠ 98 at a level of significance of 0.03 then our conclusion would be:

A. Do not reject the null hypothesis since 98 is greater than the interval limits.

B. Reject the null hypothesis since 98 falls outside the interval.

C. Reject the null hypothesis since 98 falls in the interval.

D. Do not reject the null hypothesis since 98 falls in the interval.

Answer 1

Solution:

Question 1)

Given: Suppose you reject the null hypothesis H₀: μ = 58. It turns out the population mean is actually equal to 55

If actual mean is 55 and we reject the null hypothesis H₀: μ = 58, then it means actual mean is different from 58

Thus this is a correct decision.

( Note: Type I Error : Reject H0, when H0 is True

Here statement does not say H0 is true, so this is not a Type I Error.

and Type II Error : Fail to reject H0, when H0 is False.

Here we have rejected H0, so this is not a type II Error

Hence we have made correct decision.)

Question 2)

We have created a 97% confidence interval for μ with the result [57, 97]. If we test H₀: μ=98 versus H₁: μ≠ 98 at a level of significance of 0.03 then our conclusion would be:

B. Reject the null hypothesis since 98 falls outside the interval.

We can see 98 is above the 97% confidence interval [57, 97]. So we must reject null hypothesis H0.