Question

Consider the following hypothesis test:

H₀: μ = 15

H_a: μ ≠ 15

A sample of 50 provided a sample mean of 14.17. The population standard deviation is 4.

a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 4 decimals)?

c. Using α = .05, can it be concluded that the population mean is not equal to 15?

Answer the next three questions using the critical value approach.

d. Using α = .05, what are the critical values for the test statistic? (+ or -)

e. State the rejection rule: Reject H₀ if z is

the lower critical value and is

the upper critical value.

f. Can it be concluded that the population mean is not equal to 15?

Answer 1

a)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (14.17 - 15)/(4/sqrt(50))
z = -1.47

b)

P-value Approach
P-value = 0.1416

c)

As P-value >= 0.05, fail to reject null hypothesis.

it cannot be concluded that the population mean is not equal to 15

d)

Critical value of z are -1.96 and 1.96.

e)

Hence reject H0 if z < -1.96 or z > 1.96

f)

it cannot be concluded that the population mean is not equal to 15