Respuesta :
Answer:
We conclude that the mean weekly earnings of a production worker have changed.
Step-by-step explanation:
We are given that according to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in July 2011 were $657.49.
The researcher randomly selects 52 production workers from across the United States. The resulting sample average is $672.58. Assuming a population standard deviation of $63.90
Let [tex]\mu[/tex] = mean weekly earnings of a production worker.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $657.49 {means that the mean weekly earnings of a production worker have remained same}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] $657.49 {means that the mean weekly earnings of a production worker have changed}
The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean weekly earnings = $672.58
[tex]\sigma[/tex] = population standard deviation = $63.90
n = sample of production workers = 52
So, the test statistics = [tex]\frac{672.58-657.49}{\frac{63.90}{\sqrt{52} } }[/tex]
= 1.703
The value of z test statistics is 1.703.
Now, at 10% significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.
Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean weekly earnings of a production worker have changed.
