What kind of test should I run for this question and how do I run the test? During the first 13 weeks of the television season, the Saturday evening 8:00 P.M. to 9:00 P.M. audience proportions were recorded as ABC 29%, CBS 26%, NBC 22%, and independents 23%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 91 homes, CBS 64 homes, NBC 81 homes, and independents 64 homes. Test with  = .05 to determine whether the viewing audience proportions changed. Use Table 12.4.

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Asked Dec 12, 2019
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What kind of test should I run for this question and how do I run the test?

 

During the first 13 weeks of the television season, the Saturday evening 8:00 P.M. to 9:00 P.M. audience proportions were recorded as ABC 29%, CBS 26%, NBC 22%, and independents 23%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 91 homes, CBS 64 homes, NBC 81 homes, and independents 64 homes. Test with  = .05 to determine whether the viewing audience proportions changed. Use Table 12.4.

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Expert Answer

Step 1

We will use chi-square goodness of fit statistic to test the hypothesis

Given data and calculation for expected value is shown below

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Independents | Total ABC CBS NBC Number of 91 64 81 64 300 viewers (Observed) Expected number of 300 х 0.29 300 х 0.26 300 x0.22 = 300 х0.22 — 300 = 87 = 78 66 69 viewers

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Step 2

Formulation of Hypothesis

Null Hypothesis H0: - Viewing audience proportion remains same

 Alternative Hypothesis H1: - Viewing audience proportion changed.

Test statistic is given by

The formula for the chi-square is given below

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(0; - E;)2 Σ x2 E; (64 – 78)?. (81 – 66)?. (64 – 69)? (91 – 87)2 6.468 87 78 66 69

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Step 3

Degree of freedom ...

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= (no of groups – 1) = (4 – 1) = 3 Finding the critical chi-square value CHISQ.INV.RT(0.05,3)) X6,05.3 = 7.815 ( FROM EXCEL = χ2 χ605,3

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