1- A) Claim: “The proportion of symptom-free placebo subjects is less than the p
ID: 3371010 • Letter: 1
Question
1- A)
Claim: “The proportion of symptom-free placebo subjects is less than the proportion of symptom-free subjects who received a new supplement.”
A medical researcher wants to determine if a new supplement is effective at reducing the duration of the common cold. Healthy subjects are intentionally infected with a cold-causing virus, and then given either a placebo or the new supplement one day later. Of the 267 subjects who were given a placebo, 33% were symptom-free a week later. And of the 289 subjects who were given the supplement, 56% were symptom-free after a week. Test the claim at the 0.01 significance level.
B)
0.000 067 (or 6.7×10-5)
C) Claim: “The proportion of symptom-free placebo subjects is less than the proportion of symptom-free subjects who received a new supplement.”
A medical researcher wants to determine if a new supplement is effective at reducing the duration of the common cold. Healthy subjects are intentionally infected with a cold-causing virus, and then given either a placebo or the new supplement one day later. Of the 267 subjects who were given a placebo, 33% were symptom-free a week later. And of the 289 subjects who were given the supplement, 56% were symptom-free after a week. Test the claim at the 0.01 significance level.
-5.242
D)
a. -2.33 b. -2.345 c. -2.575 d. -1.28 July 10 53 July 1July 8 June 7 45 July 25 51 Before 50 August 2 August 9 August 20 September 2 September 6 After 62 74 72 73 70Explanation / Answer
Solution:-
1)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1> P2
Alternative hypothesis: P1 < P2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.4496
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.04223
z = (p1 - p2) / SE
z = - 5.45
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than -5.45
Thus, the P-value = less than 0.0001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.01), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that the proportion of symptom-free placebo subjects is less than the proportion of symptom-free subjects who received a new supplement.
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