Question

Select the correct answer for the following two questions:

1.The length of a 95% confidence interval is _____ the length of a 90% confidence interval

A. longer than

B. equal

C. shorter than

D. half

2. if a p-value for a hypothesis test = 0.02, that means that approximately ___ of the time, we will correctly fail to reject a true null hypothesis.

A. 2%

B. 98%

C. 95%

D. 5%

Answer 1

Question 1

The length of a 95% confidence interval is longer than the length of 90% confidence interval.

(Because as confidence level increase, the critical value which we multiply to standard error increase.

Margin of error= critical value * SE. Bigger value is subtracted from mean so length of the confidence interval increase.)

Question 2

If a p value for hypothesis test=0.02, that means that approximately 95% , we will correctly fail to reject a true null hypothesis.

(Type 1 error- rejecting null hypothesis when it is true.

And 1- type 1 error is fail to reject the null hypothesis when it is true. Here type 1 error is set to 5% hence 1-0.05=0.95)