Question

The ?‑ value for a two‑sided test of the null hypothesis ?0:?=10 is 0.06 .

Question 1: Does the 95% confidence interval include the value 10 ? Why or why not?

a)No: ?=0.06 indicates that the results observed are significant at the ?=0.05 level, but this is not enough information to say a 95% confidence interval will include 10 .

b)No: ?=0.06 indicates that the results observed are significant at the ?=0.05 level, so the 95% confidence interval will not include 10 .

c)Yes: ?=0.06 indicates that the results observed are not significant at the ?=0.05 level, so the 95% confidence interval will include 10 .

d) Yes: ?=0.06 indicates that the results observed are significant at the ?=0.05 level, so the 95% confidence interval will include 10 .

Question 2. Does the 90% confidence interval include the value 10 ? Why or why not?

a) No: Because ?<0.1 , we can reject ?0:?=10 at the ?=0.10 level. The 90% confidence interval would include only those values ? for which we could not reject ?0:?=? at the ?=0.10 level.

b) Yes: Because ?<0.1 , we can reject ?0:?=10 at the ?=0.10 level. The 90% confidence interval would include those values ? for which we could reject ?0:?=? at the ?=0.10 level, which would include 10 .

c) No: Because ?<0.1 , we cannot reject ?0:?=10 at the ?=0.10 level. The 90% confidence interval would include only those values ? for which we could reject ?0:?=? at the ?=0.10 level.

d) No: Because ?<0.1 , we can reject ?0:?=10 at the ?=0.10 level. There is not enough information to say a 90% confidence interval will include 10 .

e) Yes: Because ?<0.1 , we cannot reject ?0:?=10 at the ?=0.10 level. The 90% confidence interval would include only 10 .

Answer 1

Solution:

Question 1: Does the 95% confidence interval include the value 10 ? Why or why not?

Answer:

c)Yes: ?=0.06 indicates that the results observed are not significant at the ?=0.05 level, so the 95% confidence interval will include 10 .

Explanation:

For the given scenario, we have

α = 1 - 0.95 = 0.05

P-value = 0.06

P-value > α

So, we do not reject the null hypothesis

Results observed are not significant.

Question 2. Does the 90% confidence interval include the value 10 ? Why or why not?

Answer:

d) No: Because ?<0.1 , we can reject ?0:?=10 at the ?=0.10 level. There is not enough information to say a 90% confidence interval will include 10 .

Explanation:

For the given scenario, we have

α = 1 - 0.90 = 0.10

P-value = 0.06

P-value < α

So, we reject the null hypothesis

Results observed are significant.