Example 3

EXAMPLE 3 Calculating $χ_{data}^{2}$

Suppose the observed frequencies of browser preference in Table 3 come from a survey taken this year of 200 Internet users.

Table 11.3: Table 3 Observed frequencies of browser preference in a sample of 200 Internet users

Browser	Observed frequency
Google Chrome	80
Microsoft Internet Explorer	62
Other	58

Calculate the test statistic $χ_{data}^{2}$ by comparing the observed frequencies from Table 3 with the expected frequencies calculated in Table 2 of Example 2.

Solution

The observed frequencies $O_{i}$ are found in Table 3, and the expected frequencies are given in Table 2. Table 4 then provides the quantities needed to calculate $χ_{data}^{2}$ . Then

$χ_{data}^{2} = \sum \frac{{(O_{i} - E_{i})}^{2}}{E_{i}} \approx 4 + 0 + 3.46 = 7.46$

Table 11.4: Table 4 Calculating

$χ_{data}^{2}$

Category	$p_{i}$	$O_{i}$	$E_{i}$	$O_{i} - E_{i}$	${(O_{i} - E_{i})}^{2}$	$\frac{{(O_{i} - E_{i})}^{2}}{E_{i}}$
Chrome	0.32	80	64	16	256	$\frac{{(80 - 64)}^{2}}{64} = 4$
IE	0.31	62	62	0	0	$\frac{{(62 - 62)}^{2}}{62} = 0$
Other	0.37	58	74	−16	−256	$\frac{{(58 - 74)}^{2}}{74} \approx 3.46$

NOW YOU CAN DO

Exercises 13–18.