Question

Before the hiring of an efficiency expert, the mean productivity of a firm's employees was 45.4 units per hour, with a standard deviation of 4.5 units per hour. After incorporating the changes recommended by the expert, it was found that a sample of 30 workers produced a mean of 47.5 units per hour.

Show all steps without using excel.

Answer 1

The hypothesis being tested is:

H₀: µ = 45.4 units per hour

H_a: µ > 45.4 units per hour

x = 47.5 units per hour

σ = 4.5 units per hour

n = 30 workers

The test statistic, z = (x - µ)/σ/√n

z =

The p-value for z = 2.56 is 0.0053.

Since the p-value (0.0053) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we can conclude that the mean productivity has increased.