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 an average of $30,000 per year, are well paid because the mean annual income of all blue-collar workers in the country is less than $30,000. That figure is disputed by the union, which does not believe that the mean blue-collar income is less than $30,000. To test the company president's belief, an arbitrator draws a random sample of 350 blue-collar workers from across the country and asks each to report his or her annual income. If the arbitrator assumes that the blue-collar incomes are normally distributed with a standard deviation of $8,000, can it be inferred at the 5% significance level that the company president is correct?

Explanation / Answer

here the distribution is normal

therefore the z normal hypothesis test will be done

the null hypothesis = H0= u = 33000

the alternate hypothesis = Ha= u <33000

the critical region for alpha = 0.05

= z<-1.96

the z stat = (32350 - 33000) /(8000/sqrt(350))

= -1.52

as the z stat = -1.52>-1.96

therefore we will not reject the null hypothesis

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