EXAMPLE 8.14
Sex and Instagram use: The z test. Are young women and men equally likely to say they use Instagram? We examine the data in Example 8.11 (page 507) to answer this question. Here is the data summary:
| Sex | n | X | |
|---|---|---|---|
| Women | 537 | 328 | 0.6108 |
| Men | 532 | 234 | 0.4398 |
| Total | 1069 | 562 | 0.5257 |
The sample proportions are certainly quite different, but we will perform a significance test to see if the difference is large enough to lead us to believe that the population proportions are not equal. Formally, we test the hypotheses
H0: p1 = p2
Ha: p1 ≠ p2
513
The pooled estimate of the common value of p is
Note that this is the estimate on the bottom line of the preceding data summary. The test statistic is calculated as follows:
= 5.60
The P-value is 2P(Z ≥ 5.60). Note that the largest value for z in Table A is 3.49. Therefore, from Table A, we can conclude that P < 2(1 − 0.9998) = 0.0004, although we know that the true P value is smaller.