Last year,10 percent of all teenagers purchased a new iPhone.This year,a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone.The test statistic to find out whether the percent has risen would be:

Question

Quizplus · Accepted Answer

We need to use a one-sample proportion z-test to test whether the proportion of teenagers who purchased a new iPhone has increased from 10% to some other value. The test statistic is calculated as:

z = (p̂ - p) / sqrt(p*(1-p)/n)

where p̂ is the sample proportion, p is the hypothesized population proportion (here, p=0.1), and n is the sample size.

In this case, p̂ = 39/260 = 0.15. Plugging in the values, we get:

z = (0.15 - 0.1) / sqrt(0.1*(1-0.1)/260) = 2.687

The corresponding p-value (assuming a two-tailed test) is 0.007, which is less than the standard cutoff of 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence that the proportion of teenagers who purchased a new iPhone has increased from 10%. The best choice for the test statistic is A, 2.687.

Last Year,10 Percent of All Teenagers Purchased a New IPhone