Question

A sample of 42 observations is selected from a normal population. The sample mean is 29, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: μ ≤ 28

H₁: μ > 28

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

Solution:

a)

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

b)

Critical value of  the significance level is α = 0.05, and the critical value for a one-tailed test is

= 1.645

Reject H0. if z > 1.645

c)

The test statistics,

Z =( - )/ (/n)

= ( 29 - 28 ) / ( 4 / 42 )

= 1.62

d)

Since it is observed that z = 1.62 < = 1.645, it is then concluded that the null hypothesis is fail to rejected.

e)

Do not reject

e1)

P-value = P(Z > z )

= 1 - P(Z < 1.62 )

= 0.0526

e2)

The p-value is p =0.0526, and since p = 0.0526 > 0.05, it is concluded that the null hypothesis is fail to rejected.