Question

1. Identify the correct HYPOTHESES used in a hypothesis test of the following claim and sample data:
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.

a.	H0: pplacebo = psupplement vs. H1: pplacebo > psupplement	b.	H0: μplacebo = μsupplement vs. H1: μplacebo > μsupplement
c.	H0: pplacebo = psupplement vs. H1: pplacebo < psupplement	d.	H0: μplacebo = μsupplement vs. H1: μplacebo < μsupplement

2. Identify the value of the TEST STATISTIC used in a hypothesis test of the following claim and sample data:
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.

a.	-5.242	b.	-5.447
c.	-5.470	d.	-2.255

3. Identify the value of the CRITICAL VALUE(S) used in a hypothesis test of the following claim and sample data:
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.

a.	-1.28	b.	-2.33
c.	-2.345	d.	-2.575

4. Identify the P-VALUE in a hypothesis test of the following claim and sample data:
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.

a.	0.000 000 079 4 (or 7.94×10-8)	b.	0.000 000 022 6 (or 2.26×10-8)
c.	0.024	d.	0.012

5. Identify the CONCLUSION of a hypothesis test of the following claim and sample data:
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.

a.	There is sufficient evidence to warrant rejection of the claim.	b.	There is not sufficient evidence to warrant rejection of the claim.
c.	There is sufficient evidence to support the claim.	d.	There is not sufficient evidence to support the claim.

Answer 1

1)

H₀: p_placebo = p_supplement vs. H₁: p_placebo < p_supplement

₂₎ value of the TEST STATISTIC =-5.447

3) value of the CRITICAL VALUE(S) -2.33

4)

p value =0.000 000 022 6

5)

There is sufficient evidence to support the claim.