Question

A drug company believes that at least half of all 13- to 17-year-olds with autism will repond better to a new drug therapy for autism. A random sample of 900 13- to 17-year-olds with autism found that 411 had responded better to this new drug therapy for autism. Let p be the proportion of all teens in this age range who respond better.

The test statistic for the above hypothesis test for the proportion of 13- to 17-year-olds who respond better is...

Answer 1

The test statistic for the hypothesis test for the proportion of 13- to 17-year-olds who respond better to the new drug therapy for autism is -2.721.

Step-by-step explanation:

The test statistic for the hypothesis test for the proportion of 13- to 17-year-olds who respond better to the new drug therapy for autism can be calculated using the formula:

test statistic = (sample proportion - hypothesized proportion) / standard error

Given that 411 out of 900 teens responded better, the sample proportion would be 411/900 = 0.457. The hypothesized proportion is 0.5. The standard error can be calculated as: sqrt(p * (1-p) / n), where p is the hypothesized proportion and n is the sample size. Plugging in the values, we get sqrt(0.5 * (1-0.5) / 900) = 0.0158. Substituting all the values into the test statistic formula, we get: (0.457 - 0.5) / 0.0158 = -2.721.