Question

Q2. This question is testing your understanding of some important concepts about hypothesis testing and confidence intervals. For each part below, you must explain your answer.

(a) Suppose we are performing a one-sample t test at the 10% level of significance where the

hypotheses are H0 : µ = 0 vs H1 : µ =/ 0. The number of observations is 15. What is the critical value?

(b) Suppose we are performing a one-sample t test with H0 : µ = 0 vs H1 : µ > 0. The test

statistic, 1.31, was found to be wrongly calculated. The correct test statistic should be 2.31 instead. Is the correct p-value higher than, lower than, or the same as the original one?

(c) Suppose we are performing a hypothesis test and we conclude that we can reject H0 at the

10% level of significance, can we reject the same H0 (with the same H1) at the 1% level of significance?

(d) Determine if the following statement is true or false:

H0 can always be rejected if the observed test statistic is greater than the critical value.

(e) Based on the data, we obtain (0.2, 0.6) as the 95% confidence interval for the true mean.

What can we say about the test with the hypotheses H0 : µ = 0 against H1 : µ =/ 0 at the 5% level of significance?

Answer 1

Ans

A) since n= 15

Degree of freedom = 14,level of significance = 0.10

Critical value= 1.76

B) the correct p value is lower than the original one .

C)

we can reject H0 at the

10% level of significance, can we reject the same H0 (with the same H1) at the 1% level of significance

Ans no this not always true.

D)H0 can always be rejected if the observed test statistic is greater than the critical value.

Ans true

E)since the 95%confidence interval = (0.2,0.6)

This interval does not contain zero

So we say that the there is not sufficient evidence to conclude that true mean equal to zero at 5% level of significance.