Question

# In the midst of labor-management negotiations, the president of a company argues that the company’s blue-collar...

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 \$43,000 per year, are well paid because the mean annual income of all blue-collar workers in the country is less than \$43,000. That figure is disputed by the union, which does not believe that the mean blue-collar income is less than \$43,000. To test the company president’s belief, an arbitrator draws a random sample of 225 blue-collar workers from across the country and asks each to report his or her annual income. The sample mean annual income of the 225 randomly selected blue-collar workers was \$43,318. Assume that the population standard deviation is \$5,000. Can it be inferred at the 5% significance level that the company president is correct?

1. To test: Ho: (Click to select)x¯αpβμ =   vs. Ha: (Click to select) x¯μ β αp (Click to select)><=≥≤≠

2. Test Statistic (Round to 3 decimals): z =

3. p-value (Round to 3 decimals):

Conclusion: At α = , (Click to select)reject Hado not reject Hodo not reject Hareject Ho since p-value (Click to select)><= α. We have (Click to select)sufficientinsufficient evidence to conclude that the (Click to select)sample meanpopulation variancesample proportion of thepopulation proportion of thepopulation meansample variance annual income of blue-collar workers (Click to select)is less thanis greater thanis equal todiffers from dollars.

Therefore, there (Click to select)is notis enough evidence to infer that the company president is (Click to select)incorrectcorrect

1)
H0 : mu = 43000
Ha: mu < 43000

2)

xbar = 43318 ,sigma = 5000 , n = 225

z = (xbar -mu)/(sigma/sqrt(n))
= ( 43318 - 43000)/(5000/sqrt(225))
= 0.954

3)

p value = P(z< 0.954)

p value = 0.8300

at alpha 0.05 do not reject H0 since p value> 0.05

We have insufficient evidence to conclude that the the mean annual income of all blue-collar workers in the country is less than \$43,000.

There is not enough evidence to infer that the company president is less than 430000

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