Question

The average daily yield of a chemical process has been 880 tons. A new process has been evaluated for 25 days with an average yield of 900 tons and sample standard deviation, s = 20 tons. Can one say, with 95% confidence, the process has changed?

Answer 1

df = n - 1 25 - 1 = 24

From T table,

t critical value at 0.05 significance level with 24 df = 2.064

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

900 - 2.064 * 20 / sqrt(25) < < 900 + 2.064 * 20 / sqrt(25)

891.744 < < 908.256

95% C I is ( 891.744 , 908.256 )

Since claimed mean 800 not contained in confidence interval,

We have sufficient evidence to support the claim that the process has changed.