In the midst of labor-management negotiations, the president of a company argues

Question

In the midst of labor-management negotiations, the president of a company argues that the company's blue collar workers, who are paid on an average of $33,500 per year, are well paid because the mean annual income of blue collar workers in the area is less than $33,500. That figure is disputed by the union, which believes the workers are paid less than $33,500 per year. To test the union's belief an arbitrator draws a random sample of annual income amounts from 350 blue collar workers in the area and finds the average income to be $32,850. The arbitrator assumes the incomes are normally distributed with a standard deviation of $8500. Can it be inferred at a 5% level of significance that the union's claims are correct?

Explanation / Answer

here the distribution is normal

therefore the z normal hypothesis test will be done

the null hypothesis = H0= u = 33500

the alternate hypothesis = Ha= u <33500

the critical region for alpha = 0.05

= z<-1.96

the z stat = (32850 - 33500) /(8500/sqrt(350))

= -1.43

as the z stat = -1.43>-1.96

therefore we will not reject the null hypothesis

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