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.

Answer 1

Phat1 = 9/142

Phat 2 = 5/268

Phat 3 14/410

Test statistics = (Phat 1 - Phat 2) / (Square root of (phat × (1- phat))

times the square root of (1/n1 + 1/n2))

Test statistics = 2.373

P- value = 2× (1- normal cdf (2.373, 0, 1))

= 0.0176

At the level of significance, there is difference between the proportion of drug-resistant with in the two states.