Question

A scientist claims that pneumonia causes weight loss in mice. The table shows the weights​ (in grams) of six mice before infection and two days after infection. At α= 0.01​, is there enough evidence to support the​ scientist's claim? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (e) below.

Mouse	1	2	3	4	5	6
Weight (before)	21.4	21.1	21.6	23.1	23.1	21.1
Weight (after)	20.1	20.2	20.8	22.6	22.2	19.8

Answer 1

Let us denote

d : Weight (before) - Weight (after)

Here

sample mean of difference

sample standard deviation of difference

and sample size n = 6

To test against

The test statistic can be written as

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

We reject H₀ at 0.01 level of significance if P-value < 0.01

Now,

The value of the test statistic

and P-value

Since P-value < 0.01, so we reject H₀ at 0.01 level of significance and we can conclude that there is enough evidence to support the claim.