Math CentralQuandaries & Queries


Subject: Statistics
Name: Rick
Who are you: Teacher

For many years TV executives used the guideline that 30 percent of the audience were watching each of the prime-time networks and 10 percent were watching 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 the 0.05 significance level, can we conclude that the guideline is still reasonable?

Hi Rick,

I would use the chi-square test for this problem. You have a multinomial distribution with four categories, ABC, CBS, NBC and a cable chanel. The null hypothesis is that the the percentages of the TV audience in prime-time are

30% watch ABC
30% watch CBS
30% watch NBS and
10% watch a cable station.

The alternate hypothesis is that these percentages are not correct.

You have a sample of size 500 so, under the null hypothesis the expected numbers are

500 x 0.30 = 150 watch ABC
500 x 0.30 = 150 watch CBS
500 x 0.30 = 150 watch NBS and
500 x 0.10 =   50 watch a cable station.

The observed values are

165 watch ABC
140 watch CBS
125 watch NBS and
  70 watch a cable station.

Use these values to calculate the chi-square statistic and compare this value to the 5% critical number for the chi-square distribution with (the number of categories) - 1 = 4 - 1 = 3 degrees of freedom.


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