According to the local union president, the mean gross income of the plumbers in

Question

According to the local union president, the mean gross income of the plumbers in the Salt Lake City area is normally distributes, with a mean $30,000 and a standard deviation of $2,600. A recent investigative reporter for a TV station found, for a sample of 77 plumbers, that the mean gross income was $30,500. At the 0.05 significance level can we conclude that the mean is greater than $30,000? Find the test statistic and critical value. What would the Ho and Ha be? Would you reject or fail to reject the null hypothesis?

Explanation / Answer

Ho: mean=30000

Ha: mean>30000

critical value at 0.05 level z=1.645

for std error=std deviation/(n)1/2 =296.2975

hence test stat z=(X-mean)/std error =(30500-30000)/296.2975=1.6875

as test stat is higher then critical value we reject null hypothesis

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