EXAMPLE 4 Critical-value method for the goodness of fit test

Test whether the Internet browser market shares from Example 2 have changed since June 2014, using level of significance .

Solution

  • Step 1 State the hypotheses and check the conditions. The hypotheses are:

    Checking the conditions, the expected frequencies from Table 2 are

    Because none of these expected frequencies is less than 1, and none of the expected frequencies is less than 5, the conditions for performing the goodness of fit test are satisfied.

  • Step 2 Find the critical value, , and state the rejection rule. We have degrees of freedom . Turning to the table (Table E in the Appendix) in the column labeled and the row containing , we find , as shown in Figure 1. The rejection rule is “Reject if ."

    638

    image
    Figure 11.1: FIGURE 1 Finding the critical value for and level of significance .
  • Step 3 From Example 3, we have .
  • Step 4 State the conclusion and the interpretation. Compare is greater than , as shown in Figure 2. Therefore, we reject .
    image
    Figure 11.2: FIGURE 2 Reject when

Evidence exists at level of significance that the random variable browser does not follow the distribution specified in . In other words, evidence exists that the market shares for Internet browsers have changed.

NOW YOU CAN DO

Exercises 19–22.