Question

A microbiologist wishes to determine whether there is any difference in the time it takes to make yogurt from two different starters: lactobacillus acidophilus (A) and bulgarius (B).

Seven batches of yogurt were made with each of the starters. The table below shows the time, in hours, to make each batch. Assume that both sets of times may be considered to

be random samples from normal populations. Determine whether the mean time taken to make yogurt is the same for both starters at 1% significance level.

Starter A	6.8	6.3	7.4	6.1	8.2	7.3	6.9
Starter B	6.1	6.4	5.7	5.5	6.9	6.3	6.7

(a) [1] State the null and alternative hypotheses.

(b) [1] Compute the test statistic value.

(c) [1] Find the corresponding p-value.

(d) [1] Make the decision according to (c).

(e) [1] Give the conclusion by the decision made from (d).

Answer 1

Let denote the mean time taken to make yogurt for started A and starter B respectively.

There is sufficient evidence to support the claim that the mean time taken to make yogurt is the same for both starters.