Four different holiday firms which all carried equal numbers of holidaymakers reported the following numbers who expressed satisfaction with their holiday: Firm A B C D Number satisfied 576 558 580 546 Is there any significant difference between the firms? If told that the four firms carried 600 holidaymakers each, would you modify your conclusion? What do you conclude about your first answer?

Using the data as presented, with expected values of 565, yields [latex]\chi^2(3) = 1.33[/latex], not significant. However, adding the dissatisfied customers (24, 42, 20, 54) and constructing a contingency table yields [latex]\chi^2(3) = 22.94[/latex], highly significant. The differences between the small numbers of dissatisfied customers adds most to the test statistic. The former result should be treated with suspicion since it is fairly obvious that there would be small numbers of dissatisfied customers.

Question 6.PR.5: Four different holiday firms which all carried equal numbers...

Statistics for Economics, Accounting and Business Studies

Four different holiday firms which all carried equal numbers of holidaymakers reported the following numbers who expressed satisfaction with their holiday:

Firm	A	B	C	D
Number satisfied	576	558	580	546

Is there any significant difference between the firms? If told that the four firms carried 600 holidaymakers each, would you modify your conclusion? What do you conclude about your first answer?

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Using the data as presented, with expected values of 565, yields $\chi^2(3) = 1.33$ , not significant. However, adding the dissatisfied customers (24, 42, 20, 54) and constructing a contingency table yields $\chi^2(3) = 22.94$ , highly significant. The differences between the small numbers of dissatisfied customers adds most to the test statistic. The former result should be treated with suspicion since it is fairly obvious that there would be small numbers of dissatisfied customers.