Question

A sample of 34 observations is selected from a normal population. The sample mean is 28, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: μ ≤ 26

H₁: μ > 26

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

• One-tailed test

• Two-tailed test

2. What is the decision rule?

• Reject H₀ when z > 1.645

• Reject H₀ when z ≤ 1.645

3. What is the value of the test statistic? (Round your answer to 2 decimal places.)

4. What is your decision regarding H₀?

• Reject H₀

• Fail to reject H₀

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

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

Answer 1

(A) it is a one tailed test because the alternate hypothesis include a greater than sign which means that it is a right tailed hypothesis

(B) Critical z score for 0.05 level of significance is 1.645, so we will reject the null hypothesis when the test statistic value is more than the critical value of 1.645

therefore, option. A is correct

(C) z test statistic

(D) reject Ho because the calculated z score is greater than the z critical value

(E-1) using z table, check 2.9 in the left most column and 0.02 in the top row, select the intersecting cel, we get

p value = 0.0018

(E-2) p value is less than the significance level of 0.05, we can reject the null hypothesis as the result is significant