Question

2. Last year the government made a claim that the average income of the American people was $33,950. However,
a sample of 50 people taken recently showed an average income of $34,076 with a population standard deviation
of $324. Is the government’s estimate too low? Conduct a significance test to see if the true mean is more than
the reported average. Use a significance level of 0.01.
A. Hypotheses:

B. Test Statistic

C. Critical Value

P – value: _______________

D. Decision Rule

E. Conclusion

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 33950
Alternative Hypothesis, Ha: μ < 33950

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (34076 - 33950)/(324/sqrt(50))
z = 2.75

This is left tailed test, for α = 0.01
Critical value of z is -2.326.

P-value Approach
P-value = 0.997

Hence reject H0 if z < -2.326

As P-value >= 0.01,

fail to reject null hypothesis.

There is not sufficient evidence to conclude that the government estimate is too low.