Question

Consider the following hypotheses and sample​ data, and then complete parts a and b below using α=0.05.

H0​:mu ≤17

H1​: mu >17

21, 20, 14, 19, 23, 21, 14, 19. 16, 14

a) What conclusion should be​ drawn? Determine the critical​ value(s).

The critical​ value(s) is(are)_____. ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

Determine the test​ statistic, t Subscript x overbar____. t Subscript x overbar equals____(Round to two decimal places as​ needed.)

What conclusion should be​ drawn?

A. Reject Upper H 0. There is sufficient evidence to conclude that mu greater than 17

B. Do not reject Upper H 0. There is not sufficient evidence to conclude that mu greater than 17.

C. Reject Upper H 0. There is not sufficient evidence to conclude that mu greater than 17.

D. Do not reject Upper H 0. There is sufficient evidence to conclude that mu greater than 17. ​

b) Use technology to determine the​ p-value for this test. ​p-value=_____

Answer 1

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if

a) The critical value is

The value of the test statistic =

Since , so we fail to reject H₀ at 5% level of significance and we can conclude that there is not sufficient evidence to conclude that mu greater than 17.

ans-> B. Do not reject Upper H 0. There is not sufficient evidence to conclude that mu greater than 17.

b) P-value =