Answer to Question #162640 in Statistics and Probability for Sunny

Question

According to the U.S Bureau of labor statistics, the average weekly earnings of a production worker in 1997 were $ 424.20. 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. The resulting sample average is $ 432.69. Assuming a population standard deviation of $ 33.90, and a 5% level of significance, test the hypothesis that the mean weekly earnings of a production worker have changed.

Answer 1

Answer:

Step 1

Given:

The average weekly earnings of a production worker in 1997 =$424.20

The researcher randomly selects 54 production workers

The resulting sample average=$ 432.69

H₀ :μ=424.20

H_a :μ not equal to 424.20

Thus the test statistic 

z= $432.69 - 424.20 \over ({33.90 \over √54})$

On simplifying,

z=1.84

P-value (2 tailed)=2 .P(Z>1.84)

On simplifying,

P-value=0.0658

Critical z-value=±1.96

Here the p-value is greater than 0.05 thus the condition fails therefore rejecting the null hypothesis.

There is no sufficient evidence to conclude that mean weekly earning of a production workers have changed.