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

43

of the

48

subjects treated with echinacea developed rhinovirus infections. In a placebogroup,

76

of the

90

subjects developed rhinovirus infections. Use a

0.01

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.

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 hypothesistest?

A.

H0:

p1p2

H1:

p1p2

B.

H0:

p1p2

H1:

p1=p2

C.

H0:

p1=p2

H1:

p1>p2

D.

H0:

p1p2

H1:

p1p2

E.

H0:

p1=p2

H1:

p1

F.

H0:

p1=p2

H1:

p1p2

Part 2

Identify the test statistic.

z=

(Round to two decimal places asneeded.)

Part 3

Identify theP-value.

P-value=

(Round to three decimal places asneeded.)

Part 4

What is the conclusion based on the hypothesistest?

TheP-value is greater? Or less than?

the significance level of

=0.01,

so reject? Or fail to reject?

the null hypothesis. There is? Or is not?

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

Part 5

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

The

99%

confidence interval is =_____

(Round to three decimal places asneeded.)

Part 6

What is the conclusion based on the confidenceinterval?

Because the confidence interval limits include? Or do not include?

0, there does? Or does not?

appear to be a significant difference between the two proportions. There is? Or is not?

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

Part 7

c. Based on theresults, does echinacea appear to have any effect on the infectionrate?

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

C.

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

D.

The results are inconclusive.