EXAMPLE 25 Calculating for the test for proportion

The NPD Group reported in 2013 that sales of the Chromebook accounted for 20% of the U.S. computer market. Suppose a random sample of computers found 76 that were Chromebooks. We are interested in testing whether the population proportion of Chromebooks has changed from 20%.

  1. Construct the hypotheses.
  2. Calculate the test statistic .

Solution

The key words “has changed” indicate a two-tailed test. “Changed from what?” The hypothesized proportion . The hypotheses are

The sample proportion of Chromebooks is

We then calculate the value of the test statistic :

NOW YOU CAN DO

Exercises 7–14.