3. A medical researcher examined the number of asthma attacks patients had both before andwhile using an advanced air purifier. Seven patients were included in the study. The number ofasthma attacks for each patient before and during using the air purifier is reported below. Use a05, 2-tailedDuringPurifier4PatientBeforePurifier1729831274566106754a. State the null and alternative hypotheses belowb. What type of test should be run on the data (be specific with the exact name of the test)? Forexample, don't just state "t test," but the specific t test used.c. What is the conclusion of the hypothesis test? State the p-value and the decision about thehypothesis test below. (Don't write the results here that will be done in (e) below-just state pand whether Ho is rejected.)co On ot

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Asked Nov 18, 2019
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I have attached the picture for review. Please answer section A, B, C.

3. A medical researcher examined the number of asthma attacks patients had both before and
while using an advanced air purifier. Seven patients were included in the study. The number of
asthma attacks for each patient before and during using the air purifier is reported below. Use a
05, 2-tailed
During
Purifier
4
Patient
Before
Purifier
1
7
2
9
8
3
12
7
4
5
6
6
10
6
7
5
4
a. State the null and alternative hypotheses below
b. What type of test should be run on the data (be specific with the exact name of the test)? For
example, don't just state "t test," but the specific t test used.
c. What is the conclusion of the hypothesis test? State the p-value and the decision about the
hypothesis test below. (Don't write the results here that will be done in (e) below-just state p
and whether Ho is rejected.)
co O
n ot
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3. A medical researcher examined the number of asthma attacks patients had both before and while using an advanced air purifier. Seven patients were included in the study. The number of asthma attacks for each patient before and during using the air purifier is reported below. Use a 05, 2-tailed During Purifier 4 Patient Before Purifier 1 7 2 9 8 3 12 7 4 5 6 6 10 6 7 5 4 a. State the null and alternative hypotheses below b. What type of test should be run on the data (be specific with the exact name of the test)? For example, don't just state "t test," but the specific t test used. c. What is the conclusion of the hypothesis test? State the p-value and the decision about the hypothesis test below. (Don't write the results here that will be done in (e) below-just state p and whether Ho is rejected.) co O n ot

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Expert Answer

Step 1

a)Hypotheses and level of significance:

Denote μ1 and μ2 as the mean number of asthma attacks before and while using an advanced air purifier. Thus, the difference in mean number of asthma attacks is μd = μ1μ2.

The hypotheses to be tested are:

Null hypothesis:

H0: The mean number asthma attacks are same before and while using an advanced air purifier, that is, μd = 0.

Alternative hypothesis:

H1: The mean number asthma attacks are not same before and while using an advanced air purifier, that is, μd ≠0.

The level of significance is given as α = 0.05.

Step 2

b)Paired t-test statistic:

In order to test a hypothesis regarding whether the difference between a paired set of n observations (xi, yi) is significant or not, the paired t-test is used.  Here, paired t-test is appropriate.

c) Conclusion of the hypothesis test:

The test statistic for the paired t-test is given as follows:

 

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d t = se(a) where, a--Σ(*-y). n i=1 se(d) standard error of d standard deviation of d п 1 2. Σ4-a, п —1 п

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Step 3

The following table shows the necessary calcul...

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Difference (di d-bar)2 = (di -(-3))2 Patient Before purifier During Purifier (di Before- During) 1 7 4 0 2 9 1 4 12 3 9 4 7 5 0 6 10 4 1 7 5 1 4 Total 21 18 Average 4

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