Question

Medical tests were conducted to learn about drug-resistant tuberculosis. Of cases tested in New Jersey, were found to be drug-resistant. Of cases tested in Texas, 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?

Answer 1

Yes at the level of 0.02 significance

Explanation:

we want to compare if P₁ = P₂

P1 = 9/142= 0.0634

P2 = 5/268 = 0.0187

P = 14/410 = 0.03414

significance level, α = 0.02

Test statistic, z =
`(p1 - p2)/(√((p * (1 - p) )) * ((1)/(142) * (1)/(268)))}`

Test Statistic, z =
`\frac{0.0634 - 0.0187}{\sqrt{({0.0341 * ({1 - 0.0341}})) * ({(1)/(142) + (1)/(268) ) }} } = 2.373`

Test statistic, z = 2.373

p-value = 2*p(z<|z₀|) = 2*p(z<2.37) = 0 .0176

Answer: Since p-value (0.0176) is less than the significance level, α (0.02), the null hypothesis can not hold. we can therefore say that at 0.02 level of significance, there is sufficient evidence, statistically, that p₁ is different from p₂