Question

Medical tests were conducted to learn about drug-resistant tuberculosis. Of 142 cases tested in New Jersey, 9 were found to be drug-resistant. Of 268 cases tested in Texas, 5 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 .02 level of significance. What is the p-value, and what is your conclusion?

Answer 1

Explanation:

Hello!

Sample 1 (New Jersey)

n₁= 142

x₁= 9

^ρ₁=9/142=0.063

Sample 2 (Texas)

n₂= 268

x₂= 5

^ρ₂= 5/268 = 0.0186 ≅ 0.019

Since what you need to test is if there is a significant difference between the proportions of drug-resistant cases in both states, the hypothesis are:

H₀: ρ₁-ρ₂=0

H₁: ρ₁-ρ₂≠0

α:0.20

The equation of the statistic is:

Z= (^ρ₁-^ρ₂)-(^ρ₁-^ρ₂)

√(^ρ(1-ρ)(1/n₁+1/n₂))

Where ^ρ= x₁+x₂

n₁+n₂

The calculated statistic is Z=2.2804

and the p-value= 0.0226

Since the p-value is less than the level of signification, you can reject the null hypothesis. This means that there is enough evidence to conclude that there is a significant difference between the proportion of drug-resistant tuberculosis in both states.