According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in manufacturing in the US as of October 18 was $867.60. Suppose a labor analyst wants to test to determine whether this figure is still accurate today. The analyst randomly selects 54 production workers from across the United States and obtains a representative earning statement for one week from each worker. The resulting sample average is $886.30. 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. (include all formulas, identify all variables, show all calculations, and draw and shade your distributions )

Round all calculations and enter all responses with 2 decimal places.

1. State the hypothesis:

H₀: u

H₁: u

2. What test statistic will you use?

Identify the variables for the test statistic. If a variable is unknown enter unknown (all lower case) as your answer:

a. population mean:

b. sample mean:

c. sample size:

e. population standard deviation:

f. sample standard deviation:

g. level of significance (enter as a decimal):

3. What is the critical value?

4. State the decision rule:

5. What is the test statistic you calculated?

6. Did you reject or did you not reject the null hypothesis?