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.

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