Question

Given the following hypothesis:

H0 : μ ≤ 11

H1 : μ > 11

For a random sample of 10 observations, the sample mean was 13 and the sample standard deviation 4.20. Using the .05 significance level:

(a) State the decision rule. (Round your answer to 3 decimal places.)

Reject or don't reject? H0 if t > ?

(b) Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic :

(c) What is your decision regarding the null hypothesis?

(Reject or dont reject?) H0. The mean (is or is not) greater than 11.

Answer 1

Solution :

= 11

=13

S =4.20

n = 10

This is theright tailed test .

The null and alternative hypothesis is ,

H0 :    ≤ 11

Ha : > 11

a ) Test statistic = t

= ( - ) / S / n

= (13 - 11) / 4.20 / 10

= 1.506

Test statistic = t = 1.51

b ) It is observed that t =1.506 ≤ tc​=1.833, it is then concluded that the null hypothesis is not rejected

P-value =0.0832

= 0.05  

P-value ≥

0.0832 ≥ 0.05

c )Do not reject the null hypothesis .

There is insufficient evidence to suggest that