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. hint: make sure that you carry 4 decimals for your intermediate workings.

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 wihtin the two states.