According to the U.S. Bureau of Labor Statistics, all workers in America who had

Question

According to the U.S. Bureau of Labor Statistics, all workers in America who had a bachelor’s degree and were employed earned an average of $1234 a week in 2014. A recent sample of 364 American workers who have a bachelor’s degree showed that they earn an average of $1258 per week. Suppose that the population standard deviation of such earnings is $123.

a. Find the p-value for the test of hypothesis with the alternative hypothesis that the current mean weekly earning of American workers who have a bachelor’s degree is higher than $1234. Will you reject the null hypothesis at =0.025?

Round your answer to four decimal places.

1) p-value =

2) reject or do not reject H0?

b. Test the hypothesis of part a using the critical-value approach and =0.025.

Round your answer for the observed value of z to three decimal places.

1) z =

2) reject or do not reject H0?

Explanation / Answer

H0 : u = 1234

H1 : u > 1234

a) p value = p [Z > 3.723] = 0.0000

Reject H0, since p value < 0.025

b) Z statistic = 1258 - 1234 / [123/sqrt(364)] = 3.723

Reject H0, since Z statistic > 1.96

we conclude that there is sufficient evidence that the current mean weekly earning of American workers who have a bachelor’s degree is higher than $1234

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