Question

For a fixed , if a is changed from 10 to 05, which of the following is true? A. The probability of a type I error goes down. OB. The probability of a type II error goes down. OC. The p-value goes down D. Both A and B are true E. None of the above are true. QUESTION 22 A government report says that a 99% confidence interval for the mean income of American households is ($58,711, $59.423). Using this confidence interval to test How = 59,450 versus Hau59,450 at the 1% level of significance would lead me to A fail to reject Ho B. fail to reject Ha OC.reject Ho OD. reject Ha

Answer 1

Q21) -

We know that -

$\alpha$ = Probability of type I error

If value of $\alpha$ is less, probability of type I error also decreases.

So, if $\alpha$ is changed from 0.10 to 0.05, then probabillity of type I error goes down.

$\beta$ - Probability of type II error

If value of $\alpha$ is lower, it may increase probability of type II error.

So, if $\alpha$ is changed from 0.10 to 0.05, then probabillity of type II may increase.

p-value -

P-value measures the probability of getting more extreme value than one you got in the experiment. So, it depends on the test statistic. So, value of $\alpha$ doesnot affect p-value.

So, if $\alpha$ is changed from 0.10 to 0.05, then p-value remains unchanged.

Hence, option A is correct.

Q22) -

Given 99% confidence interval for the mean income of American households is ($58711, $59423).

H₀ : $\mu$ = 59450

H_a : $\mu$ $\neq$ 59450

Value of $\mu$ idoes not lies between 99% confidence interval, this implies that $\mu$ $\neq$ 59450.

Hence, We have to reject H₀ at 1% level of significance.

Option C is correct.