Question

A sample of 30 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: μ ≤ 20

H₁: μ > 20

1. Is this a one- or two-tailed test?

• "One-tailed"—the alternate hypothesis is greater than direction.

• "Two-tailed"—the alternate hypothesis is different from direction.

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 your decision regarding H₀?

• Reject

• Do not reject

5. What is the p-value? (Round your answer to 4 decimal places.)

Answer 1

Solution:

a)

"One-tailed"—the alternate hypothesis is greater than direction.

b)

= 0.05

Right tailed test

Critical value is = = 1.65

Decision Rule : Reject H₀ if z > 1.65

c)

z =

= (21 - 20) / (6/30)

= 0.91

Test statistic z = 0.91

d)

Do not reject

e)

For right tailed test ,

p value = P(Z > z) = P(Z > 0.91) = 1 - P(Z < 0.91) = 1 - 0.8186 = 0.1814

p value is 0.1814