Question

A researcher reports that the average salary of teachers is $42,000. A sample of 30 teachers has a mean salary of $43,260. At alpha =0.05, conduct the appropriate test to determine if the teacher earn more than $42,000 a year. The standard deviation of the population is $5320. Show each of 5 steps.

Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

H0: µ = 42000 versus Ha: µ > 42000

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 42000

Xbar = 43260

σ = 5320

n = 30

α = 0.05

Critical value = 1.6449

(by using z-table or excel)

Z = (43260 - 42000)/[5320/sqrt(30)]

Z = 1.2972

P-value = 0.0973

(by using Z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the teacher earn more than $42,000 a year.