In exercises that call for two-sample procedures, you may use either of the two approximations for the degrees of freedom that we have discussed: the value given by your software or the smaller of and . Be sure to state clearly which approximation you have used.

Question 7.49

7.49 Advertising in sports.

Can there ever be too many commercials during a sporting event? A group of researchers compared the level of acceptance for commercials between NASCAR and NFL fans.24 Each fan was asked a series of 5-point Likert scale questions to evaluate their level of commercial acceptance. The average of these questions was used as the response, where a lower score means less acceptance. Here are the results:

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Group
NASCAR 300 3.42 0.84
NFL 302 3.27 0.81
  1. Is it appropriate to use the two-sample procedures that we studied in this section to analyze these data for group differences? Give reasons for your answer.
  2. Describe appropriate null and alternative hypotheses for comparing NASCAR and NFL average commercial acceptance levels.
  3. Carry out the significance test using . Report the test statistic with the degrees of freedom and the -value. Write a short summary of your conclusion.

7.49

(a) Yes, because outliers are not possible and , the procedures can be used. (b) (c) . The data are significant at the 5% level, and there is evidence of a difference between NASCAR and NFL average commercial acceptance levels.