Question

According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in manufacturing in the United States as of October 2014 was $827.27. Suppose a labor researcher wants to test to determine whether this figure is still accurate today. The researcher randomly selects 54 production workers from across the United States and obtains a representative earnings statement for one week from each worker. The resulting sample average is $843.56. Assuming a population standard deviation of $63.90 and a 5% level of significance, determine whether the mean weekly earnings of a production worker have changed.

Answer 1

Answer)

As the population s.d is known here we can use standard normal z table to conduct the test

Null hypothesis Ho : u = 827.27

Alternate hypothesis Ha : u not equal to 827.27

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Z = (843.56 - 827.27)/(63.9/√54) = 1.87

From z table, P(z>1.87) = 0.0307

As the given test is two tailed

P-value = 2*0.0307 = 0.0614

As the obtained p-value is greater than the given significance 0.05 (5%)

We fail to reject the null hypothesis Ho

So, we do not have enough evidence to conclude that the mean has changed