Question

A sample of 45 observations is selected from a normal population. The sample mean is 27, and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ ≤ 26 H1: μ > 26

2. What is the decision rule? (Round your answer to 2 decimal places.)
3. What is the value of the test statistic? (Round your answer to 2 decimal places.)
4. What is the p-value? (Round your answer to 4 decimal places.)

Answer 1

H0: μ ≤ 26 H1: μ > 26

n = 45

= 27

= 6

Use = 0.05

b) observe that ,there is > sign in H1. So , the test is right tailed.

So the critical value is i.e. _0.05

i.e. 1.65 (Use z table to find this value)

Rejection region is z >   i.e. z > 1.65

Decision Rule : Reject H0 if z > 1.65

c)The test statistic z is given by

z =

= (27 - 26) / (6/45)

= 1.12

The value of the test statistic z is 1.19

d)For right tailed test :

p value = P(Z > 1.12)

= P(Z < -1.12)

= 0.1314 (use z table)

p value is 0.1314