Question

Each year, more than 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In particular, the Centers of Disease Control and Prevention have launched studies of drug-resistant gonorrhea.† Suppose that, of 205 cases tested in a certain state, 13 were found to be drug-resistant. Suppose also that, of 429 cases tested in another state, 8 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? Use a 0.02 level of significance. (Let p₁ = the population proportion of drug-resistant cases in the first state, and let p₂ = the population proportion of drug resistant cases in the second state.)

State the null and alternative hypotheses. (Enter != for ≠ as needed.)

H₀:

H_a:

Find the value of the test statistic. (Round your answer to two decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

What is your conclusion?

A. Reject H₀. There is a significant difference in drug resistance between the two states.

B. Do not reject H₀. There is not a significant difference in drug resistance between the two states.  

C. Reject H₀. There is not a significant difference in drug resistance between the two states.

D. Do not reject H₀. There is a significant difference in drug resistance between the two states.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 != p2

p1cap = X1/N1 = 13/205 = 0.0634
p1cap = X2/N2 = 8/429 = 0.0186
pcap = (X1 + X2)/(N1 + N2) = (13+8)/(205+429) = 0.0331

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.0634-0.0186)/sqrt(0.0331*(1-0.0331)*(1/205 + 1/429))
z = 2.95

P-value Approach
P-value = 0.0032
As P-value < 0.02, reject the null hypothesis.

A. Reject H0. There is a significant difference in drug resistance between the two states.