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

1. entifying the claim and H0 and Ha,

The hypothesis being tested is:

H0: µd = 0

Ha: µd ≠ 0

1. Finding the appropriate standardized test statistic,

t = 6.455

1. Finding the P-value or the rejection region,

P-value = 0.0013

1. Deciding whether to reject or fail to reject the null hypothesis, and

Since the p-value (0.0013) is less than the significance level (0.05), we can reject the null hypothesis.

1. Interpreting the decision in the context of the original claim.

Therefore, we can conclude that µd ≠ 0.

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.

The hypothesis being tested is:

H0: µd = 0

Ha: µd > 0

The p-value is 0.0007.

Since the p-value (0.0007) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we can conclude that pneumonia causes weight loss in mice.

Before	After
19.8	18.4
20.2	19.6
19.9	19.1
22.1	20.7
23.4	22.2
23.6	23
	21.5000	mean Before
	20.5000	mean After
	1.0000	mean difference (Before - After)
	0.3795	std. dev.
	0.1549	std. error
	6	n
	5	df
	6.455	t
	.0007	p-value (one-tailed, upper)

Before	After
19.8	18.4
20.2	19.6
19.9	19.1
22.1	20.7
23.4	22.2
23.6	23
	21.5000	mean Before
	20.5000	mean After
	1.0000	mean difference (Before - After)
	0.3795	std. dev.
	0.1549	std. error
	6	n
	5	df
	6.455	t
	.0013	p-value (two-tailed)