Question

Twenty children are selected for a study on daily soda and milk consumption. The differences in consumption (Soda minus Milk) have a mean of 20 ml with a standard deviation of 33 ml.

At the 5% level of significance, we would like to determine if there is evidence that the true mean amounts of milk and soda consumed differ. What is the P-value for the appropriate test of significance?

Question 3 options:

	between 0.005 and 0.01
	between 0.01 and 0.02
	between 0.02 and 0.04
	between 0.04 and 0.05
	between 0.05 and 0.10

Answer 1

Let denotes the average difference in amounts of milk and soda consumed.

To test against

Here

sample mean of difference

sample standard deviation

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 5% level of significance if P-value < 0.05

Now,

The value of the test statistic

and P-value

So, P-value is between 0.01 and 0.02