Question

The daily yield for a chemical plant has averaged 880 tons for the last several

years. It was known previously that the standard deviation is 21 tons. The quality

control manager would like to know whether this average has changed in recent

months. She randomly selects 50 days from the computerdatabase and computes the

average of the n = 50 yields as 871 tons. Test the appropriate hypothesis using alpha   

equal to 0.05.

Answer 1

this a one sample Z-test since population std dev is known

given

= 880 tons

= 21 tons

Sample statistics n = 50

= 871

Hypothesis

H₀ : = 880 tons

H₁ : 880 tons ( two tailed test)

Level of significance = 0.05

test statistic Z = = -3.030

critical value = Z_0.025 = 1.960

Since | Z | > Z_0.025 we reject null hypothesis and conclude that there is a significant evidence that average yield has changed in recent months.