Question

A sample of 41 observations is selected from a normal population. The sample mean is 26, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: μ ≤ 25

H₁: μ > 25

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 3 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

1. e-1. What is the p-value? (Round your answer to 4 decimal places.)

1. e-2. Interpret the p-value? (Round your answer to 2 decimal places.)

Answer 1

Given,

X_bar = 24

n = 41

= 4

1) Hypothesis :

H₀: 25

H₁: > 25

2) one tailed - the alternative hypothesis is greater than direction.

3) test statistic Z = (x_bar-​​​​​​) /(/n)

= (24-25)/(4/41)

Test statistic = -1.60

4) critical value t_c for 0.05 level of significance is 1.684

5) conclusion:

t= -1.60 < t_c=1.684 since it is concluded that the null hypothesis is not rejected.

6) p value for Z test statistic is 0.9414.

P value = 0.9414

7) conclusion :

The p value (0.9414) is greater than 0.05 hence do not reject null hypothesis.