Question

1. A trade union in a factory has proposed an extension of 10 minutes of rest to workers in the hope of increasing the daily productivity of the factory. Prior to the addition of rest time, the average productivity of each employee was 240 unit per day with a standard deviation of 25 unit per day. After an additional 10-minute break was implemented, the union recorded a productivity record for each employee for 30 days at random and found that the average productivity per employee was 251 unit per day. Is there evidence at the 5% significance level that the daily productivity of factory workers has increased?

Answer 1

Stating the hypotheses:

H₀: $\mu=240$

H₀: $\mu>240$

Computing the test value:

$z=\frac{X-\mu}{\sigma/\sqrt{n}}=\frac{251-240}{25/\sqrt{30}}=2.41$

P-value = P(x>z) = 0.00798

Since the P-value is less than 0.05, the decision is to reject the null hypothesis.

There is enough evidence to support the claim that the daily productivity of factory workers has increased.