Suppose the average weekly earnings of a production worker in 1997 were $424.20. A researcher randomly selects 54 production workers and obtains a representative earnings statement for one week from each worker. Assuming the population standard deviation is $33.90.

Suppose the researcher wants to determine whether the average weekly earnings figure of $424.20 is still accurate today, with the information that the sample average of the 54 randomly selected workers is $432.69. Determine whether the mean weekly earnings of production workers has changed, using a 1% level of significance.

Step 1: Set up null and alternative hypotheses.

H₀

H₁

Step 2: Decide on significance level.

a =

Step 3: Write down the relevant information.

Calculate the value of the test statistic.

Step 4: State the decision rule. Decide whether H₀ is to be rejected or not rejected.

Step 5: Draw an appropriate conclusion