Question

In: Statistics and Probability

A scientist claims that pneumonia causes weight loss in mice. The table shows the weights​ (in...

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

alphaαequals=0.050.05​,

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)

22.622.6

19.519.5

22.622.6

23.423.4

21.921.9

22.622.6

Weight​ (after)

22.522.5

19.619.6

22.522.5

23.323.3

21.921.9

22.522.5

Solutions

Expert Solution

The table given below ,

Mouse Weight (before) (X) Weight (after)(Y) di=X-Y di^2
1 22.6 22.5 0.1 0.01
2 19.5 19.6 -0.1 0.01
3 22.6 22.5 0.1 0.01
4 23.4 23.3 0.1 0.01
5 21.9 21.9 0 0
6 22.6 22.5 0.1 0.01

From table ,

Let ,

Hypothesis : VS (Claim)

The test statistic is ,

The critical value is ,

; From Excel "=TINV(2*0.05,5)"

Decision : Here , the value of the test statistic does not lies in the rejection region

Therefore , fail to reject the null hypothesis.

Conclusion : Hence , there is not sufficient evidence to support the scientist claim that the pneumonia causes weight loss in mice.


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