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 174 cases tested in a certain state, 11 were found to be drug-resistant. Suppose also that, of 375 cases tested in another state, 7 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?

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

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

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

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

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses:

Ho: p1 = p2

Ha: p1 != p2

Test statistic = 2.73

p - Value = 0.0064

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