Question

Consider the following hypothesis test:

H₀ : μ = 16

H_a : μ ≠ 16

A sample of 50 provided a sample mean of 14.34. The population standard deviation is 7. 

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 1?

d. Using α = .05, what are the critical values for the test statistic (to 2 decimals)?

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 16?

Answer 1

a)

H₀: μ = 16

H₁: μ ≠ 16

x̅ (sample mean) = 14.34

n (sample size) = 50

σ (population standard deviation) = 7

Test Statistic = x̅ - μ / σ/√n

Test Statistic = -1.6768

b) α = 0.05

Left-tailed area corresponding to z-score of -1.6768 = 0.04678

Right-tailed area corresponding to z-score of 1.67685 = 0.04678

p-value = Left-Tailed Area + Right-Tailed Area = 0.0936

p-value is greater than α.

c) p-value is greater than α then do not reject the null hypothesis.

d) using 0.05 and degrees of freesom

Critical value (1-tailed) = 1.677.