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As sample of 105 sanitation workers for the city of Euonymus, Texas, earns an average of $24,375 per year. The average salary for all Euonymus city workers is $24,230, with a standard deviation of $523. Are the sanitation workers overpaid? Conduct both one- and two-tailed tests.

Respuesta :

The average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.

What are the null hypothesis and alternative hypothesis?

The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.

We have:

Average x = 24375

u = 24230

SD = 523

n = 105

Null hypothesis and alternative hypothesis for one-tail test:

H0: the average salary of sanitation workers in the city of Euonymus is not overpaid.

u = 24230

H1:  the average salary of sanitation workers in the city of Euonymus is overpaid.

u > 24230

Assume significance level = 0.05

From the Z-table:

Z(critical) = 1.645

Now,

Z = (x-u)/(SD/√n)

Z = (24375-24230)/(523/√105)

Z = 2.84

Z > Z(critical)

So, reject the null hypothesis.

The average salary of sanitation workers in the city of Euonymus is overpaid.

Now, from the two-tail test:

Null hypothesis and alternative hypothesis for one-tail test:

H0: the average salary of sanitation workers in the city of Euonymus is 24230

u = 24230

H1:  the average salary of sanitation workers in the city of Euonymus is not 24230

u ≠ 24230

Assume significance level = 0.05

From the Z-table for the two-tail test:

Z(critical) = ±1.96

Now,

Z = 2.84

Z > z(critical)

∴ The average salary of sanitation workers in the city of Euonymus is not 24230.

Thus, the average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.

Learn more about the null hypothesis and alternative hypothesis here:

brainly.com/question/27335001

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