A dairy farmer claims that his milk bottles contain exactly 1l of milk. A consumer took a random sample of 20 bottles & found the average contents to be 0.980l with s.d of 0.07l. Test the claim at 5%.

Question

Hypothesis test

Answer 1

The null hypothesis H0: mean=1 litre

The alternative hypothesis Ha: mean≠1 litre

Significance level ɑ=0.05 (2-tail), so we use ɑ/2 for each tail.

Test statistic T=(0.98-1)/(0.07/√20)=-1.278.

The critical value for a 2-tail t-test with 20-1=19 dof is 2.093. We compare -1.278 with left tail -2.093, and since the test statistic is greater than the critical value we conclude that there is insufficient evidence to reject H0, with a 95% degree of confidence. We cannot reject the farmer’s claim.