Question

Advertisements claim that Happy Joe's puts more pepperoni on its pizzas than competitors. In order to investigate this claim, 9 medium pizzas from Happy Joe's and 9 medium pizzas from Pizza Hut are purchased at random times over a month long period. The number of slices of pepperoni on each pizza is then counted. At � = 0.10, can you support the claim?

Happy Joe’s 25 20 21 24 23 24 26 25 21

Pizza Hut 18 22 18 19 18 22 21 19 20

Answer 1

Let us denote

d : Number of pepperoni in pizza from Happy Joe's - Number of pepperoni in pizza from Pizza Hut

To test against

Here

sample mean of difference

sample standard deviation of difference

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 10% level of significance if

Now,

The value of the test statistic =

and critical value =

Since , so we reject H₀ at 10% level of significance and we can conclude that the there is enough evidence to support the claim.