8. 3. 2. 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) 21.9 21.7 20.3 22.2 20.7 22.3 Weight (after) 20.5 21.0 19.6 21.7 19.8 21.0 (a) Identify the claim and state
8. 3. 2. 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) 21.9 21.7 20.3 22.2 20.7 22.3 Weight (after) 20.5 21.0 19.6 21.7 19.8 21.0 (a) Identify the claim and state
8. 3. 2. 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) 21.9 21.7 20.3 22.2 20.7 22.3 Weight (after) 20.5 21.0 19.6 21.7 19.8 21.0 (a) Identify the claim and state
8. 3. 2. 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)
21.9
21.7
20.3
22.2
20.7
22.3
Weight (after)
20.5
21.0
19.6
21.7
19.8
21.0
(a) Identify the claim and state
H0
and
Ha.
What is the claim?
A.
Weight loss causes pneumonia in mice.
B.
Pneumonia causes weight loss in mice.
C.
Weight gain causes pneumonia in mice.
D.
Pneumonia causes weight gain in mice.
Let
μd
be the hypothesized mean of the difference in the weights
(before−after).
What are
H0
and
Ha?
A.
H0:
μd≥d
Ha:
μd<d
B.
H0:
μd=0
Ha:
μd≠0
C.
H0:
μd≤d
Ha:
μd>d
D.
H0:
μd≤0
Ha:
μd>0
E.
H0:
μd≠0
Ha:
μd=0
F.
H0:
μd≥0
Ha:
μd<0
(b) Find the critical value(s) and identify the rejection region(s).
Select the correct choice below and fill in any answer boxes to complete your choice.
(Round to three decimal places as needed.)
A.
t>
B.
t<
C.
t<
or
t>
(c) Calculate
d
and
sd.
d=
(Round to three decimal places as needed.)
Calculate
sd.
sd=
(Round to three decimal places as needed.)
(d) Find the standardized test statistic t.
t=
(Round to three decimal places as needed.)
(e) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.
(1)
the null hypothesis. There
(2)
enough evidence to
(3)
the claim that
(4)
causes
(5)
in mice.
(1)
Reject
Fail to reject
(2)
is
is not
(3)
support
reject
(4)
weight gain
weight loss
pnuemonia
(5)
pnuemonia
weight gain
weight loss
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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