Question

! For the following cases, you may use either the P-value approach or the rejection region approach to present a full hypothesis test, including:

1. Identifying the claim and H₀ and H_a,
2. Finding the appropriate standardized test statistic,
3. Finding the P-value or the rejection region,
4. Deciding whether to reject or fail to reject the null hypothesis, and
5. Interpreting the decision in the context of the original claim.

1. A scientist claims that pneumonia causes weight loss in mice.  The table below shows weight, in grams, of six mice before infection with pneumonia and two days after infection.  At α = 0.01, evaluate the scientist’s claim.

Before After

Mouse 1           19.8     18.4

Mouse 2           20.2     19.6

Mouse 3           19.9     19.1

Mouse 4           22.1     20.7

Mouse 5           23.4     22.2

Mouse 6           23.6     23.0

Answer 1

Ans:

	Before	after	d
1	19.8	18.4	-1.4
2	20.2	19.6	-0.6
3	19.9	19.1	-0.8
4	22.1	20.7	-1.4
5	23.4	22.2	-1.2
6	23.6	23	-0.6
		d-bar	-1.000
		sd	0.379

Let d=after-before

a)Claim: pneumonia causes weight loss in mice

(claim)

Ha is claim.

b)

Test statistic:

t=(-1.00-0)/(0.379/sqrt(6))

t=-6.45

c)

df=6-1=5

p-value=P(t<-6.45)=tdist(6.45,5,1)=0.0007

d)

As,p-value<0.01,we reject the null hypothesis.

e)

There is sufficient evidence to support the claim that pneumonia causes weight loss in mice.