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 percentage has risen would be:

Question

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To test whether the percentage has risen, we need to perform a hypothesis test.

Null hypothesis: The percentage of teenagers who purchased a new iPhone is still 10%. 
Alternative hypothesis: The percentage of teenagers who purchased a new iPhone has increased.

We can use a one-tailed, two-sample z-test for proportions to test this hypothesis.

The test statistic can be calculated as:

z = (p - P) / sqrt(P(1-P)/n)

where p is the sample proportion (39/260), P is the null hypothesis proportion (0.1), and n is the sample size (260).

Plugging in the values, we get:

z = (0.15 - 0.1) / sqrt(0.1*0.9/260) = 2.687

Since this is a one-tailed test (we are only interested in whether the proportion has increased), we can compare our test statistic to the one-tailed critical value at α = 0.05.

The critical value for a one-tailed test at α = 0.05 is 1.645. Since our test statistic (2.687) is greater than the critical value (1.645), we can reject the null hypothesis and conclude that the percentage of teenagers who purchased a new iPhone has increased.

Last Year, 10 Percent of All Teenagers Purchased a New