Question

You’re the manager of the canning line at Avery Brewing Company. When the machines are operating properly, at least 12 ounces of beer is added to each can. A sample of 40 beers from the line yields a mean of 12.05 ounces with a standard deviation of 0.2 ounces. Do you think the canning line is operating properly?

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H₀: µ ≥ 12 versus H_a: µ < 12

This is a lower tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 12

Xbar = 12.05

S = 0.2

n = 40

df = n – 1 = 39

α = 0.05

Critical value = -1.6849

(by using t-table or excel)

t = (12.05 – 12)/[0.2/sqrt(40)]

t = 1.5811

P-value = 0.9390

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the machines are operating properly.