The average weekly earnings of a production worker in 2000 were AUD425. Suppose a labor researcher wants to test to determine whether this figure is still accurate today. The researcher randomly selects 50 production workers and obtains a representative earnings statement for one week from each. The resulting sample average is AUD431.0.

Assuming a population standard deviation of AUD32.2, and a 5% level of significance, determine whether the mean weekly earnings of a production worker have changed.

Determine the critical value z_c and the z score value based on the sample data?