For many years TV executives used the guideline that 30% of the audience were wa

Question

For many years TV executives used the guideline that 30% of the audience were watching each of the prime-time networks and 10% were watching the cable stations on a weekday night. A random sample of 500 viewers in the Tampa-St. Petersburg, Florida, area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station. At .05 significance level, can we conclude that the guideline is still reasonable?

Explanation / Answer

H0 : The guideline is reasonable (that is to say, same ratios still apply, or ABC = CBS = NBC = 30 %, rest = 10 % ) H1: The guideline is not reasonable (the ratios do not apply) Use the Chi square test (?^2). Why? Check your textbooks. :) Sample values are: ABC = 165 CBS = 140 NBC = 125 rest = 70 Expected values (if the given ratios still stand) ABC = 30 % * 500 = 150 CBS = 30 % * 500 = 150 NBC = 30 % * 500 = 150 rest = 10 % * 500 = 50 df = 4 - 1 = 3 (where df stands for degrees of freedom, and 4 stands for the number of stations) Using this formula: http://www.sixsigmafirst.com/chi_square_… calculate the value of ?^2. fi are the values you obtained from the sample (165, 140, 120, 70), and f'i are expected values. You can obtain the critical value of ?^2 for 3 degrees of freedom and a = 0.05 from the tables for ?^2 distribution (my tables say it's 7.815). After you've found it, compare it to the calculated value of ?^2. If the calculated value of ?^2 is lower than the table value, H0 stands. If not, you could say that, with confidence of 0.95, we claim the guidelines to be untrue.

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