Question

Massachusetts’ records show that the average household income was $ 69, 000 in 5 years ago. The state governor wants to claim that the average income has increased since 5 years ago. The state office surveyed 120 household income randomly and get a average household income $ 74, 000. Assume that the standard deviation(s) of the average household income has not been affected by the addition of the polymer and is still $ 15000. Can the state governor claim that the average household income has a statistically significant increase compare to five years ago? Use the one-sided alternative test at the significance level α = 0.05.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 69000
Alternative Hypothesis, Ha: μ > 69000

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.645.
Hence reject H0 if z > 1.645

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (74000 - 69000)/(15000/sqrt(120))
z = 3.65

P-value Approach
P-value = 0.0001
As P-value < 0.05, reject the null hypothesis.

yes, the state governor claim that the average household income has a statistically significant increase compare to five years ago