Chapter 9 problems of statistics

Question

A medical researcher claims that less than 20% of American adults are allergic to Penicillin. In a random sample of 100 adults, 18 of them say they have such an allergy. Test the researcher's claim at   . Assume that the original population is normally distributed.

 

1) State the null and alternative hypotheses

A)       B)   

C)     D)   

Answer A, B, C, or D in the box

Ho: 

H1: 

2) Compute test statistics. Round the answer to one decimal place.

Test statistics = 

3) Compute the P value. Round your answer to four decimal places.

P value = 

4) Compute the critical value. Round your answer to three decimal places. 

 Critical Value = 

5) Decision

E) Reject the Ho

F) Do not reject the Ho

Type E or F in the box 

6) Conclusion

G) There is enough evidence to support the claim that less than 20% of American adults are allergic to Penicillin.

H) There is not enough evidence to support the claim that less than 20% of American adults are allergic to Penicillin.

Type G or H in the box 

Answer 1

Ho: p = 0.20

Ha: p < 0.20

sample proportion = 18/100 = 0.18

test statistic = z = (0.18-0.2)/sqrt(0.2*0.8/100) = -0.5

p-value = P(z < -0.5) = 0.3085

critical value = z-score for 0.05 probability = -1.645

do not reject Ho (as test statistic not less than CV and p-value is greater than alpha = 0.05)

H) There is not enough evidence to support the claim that less than 20% of American adults are allergic to Penicillin.