Answer to Question #200492 in Statistics and Probability for Utsav Kafle

Question

According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in 1997 were $421.20. Suppose a labor wants to test to determine whether this figure is still accurate today. The researcher randomly selects 60 production workers from across the United States and obtains a representative earning statement for one week from each. The resulting sample average is $435.70. Assuming a population standard deviation of $33, and a 5% level of significance, determine whether the mean weekly earning of a population worker has changed.

Answer 1

$H_0:$ $\mu=421.20$

$H_{\alpha}:$ $\mu\ne421.20$

$z=\frac{\overline{}m-\mu}{\sigma/\sqrt{n}}=\frac{435.70-421.20}{33/\sqrt{60}}=3.40$

p-value:

$2P(z>3.40)=2(1-0.99966)=0.00034$

Since p-value less than level of significance, we can reject the null hypothesis.

So, the mean weekly earning of a population worker has changed.