Question

Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea,

4343

of the

4848

subjects treated with echinacea developed rhinovirus infections. In a placebo​ group,

8181

of the

9898

subjects developed rhinovirus infections. Use a

0.050.05

significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts​ (a) through​ (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with a placebo. What are the null and alternative hypotheses for the hypothesis​ test?

A.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H 1H1​:

p 1p1equals=p 2p2

B.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

C.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

D.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1less than<p 2p2

E.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

F.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1greater than>p 2p2

Identify the test statistic.

zequals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is

▼

greater than

less than

the significance level of

alphaαequals=0.050.05​,

so

▼

fail to reject

reject

the null hypothesis. There

▼

is

is not

sufficient evidence to support the claim that echinacea treatment has an effect.

b. Test the claim by constructing an appropriate confidence interval.

The

9595​%

confidence interval is

nothingless than<left parenthesis p 1 minus p 2 right parenthesisp1−p2less than<nothing.

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits

▼

include

do not include

​0, there

▼

does not

does

appear to be a significant difference between the two proportions. There

▼

is not

is

evidence to support the claim that echinacea treatment has an effect.

c. Based on the​ results, does echinacea appear to have any effect on the infection​ rate?

A.

Echinacea does appear to have a significant effect on the infection rate. There is evidence that it lowers the infection rate.

B.

Echinacea does appear to have a significant effect on the infection rate. There is evidence that it increases the infection rate.

C.

Echinacea does not appear to have a significant effect on the infection rate.

D.

The results are inconclusive.

Click to select your answer(s).

Answer 1