Question

In: Statistics and Probability

Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 42 of...

Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 42 of the 49 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group, 88

of the 105. subjects developed rhinovirus infections. Use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts​ (a) through​ (c) below.

Test the claim using a hypothesis test.

Upper H 0H0​:

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

reject

fail to 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

do not include

include

​0, there

does

does not

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

is

is not

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 increases the infection rate.

B.

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

C.

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

D.

The results are inconclusive.

p 1p1less than or equals≤p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

B.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1greater than>p 2p2

C.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1less than<p 2p2

D.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

E.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

F.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H 1H1​:

p 1p1equals=p 2

Solutions

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