Question

Given the following hypotheses:

H0: μ ≤ 10

H1: μ > 10

A random sample of 10 observations is selected from a normal population. The sample mean was 11 and the sample standard deviation 3.2. Using the 0.100 significance level:

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

Reject H0 if t >

b.	Compute the value of the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic

c.	What is your decision regarding the null hypothesis?

(Click to select)Cannot rejectReject H0. There is (Click to select)sufficientinsufficient evidence to conclude that the

Answer 1

Solution :

= 10

=11

s =3.2

n = 10

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   ≤ 10

H_a :    > 10

Test statistic = z

= ( - ) / s / n

= (11-10) / 3.2 / 11

= 0.988

a ) It is observed that t = 0.988 ≤ tc​ =1.833, it is then concluded that the null hypothesis is not rejected

b ) The test statistic t is = 0.988

c ) P-value = 0.1744

= 0.100

P-value <

0.1744 > 0.100

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean \muμ is greater than 10, at the 0.100 significance level.