{Exercise 12.03} During the first 13 weeks of the television season, the Saturda

Question

{Exercise 12.03}
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 28%, NBC 25%, and independents 18%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 99 homes, CBS 76 homes, NBC 88 homes, and independents 37 homes.

Test with  = .05 to determine whether the viewing audience proportions changed.

1. Compute the value of the 2 test statistic (to 2 decimals).
  
2. The p value is

3. Has a significant change occurred in viewing audience proportions?

Explanation / Answer

null hypothesis:Ho:  viewing audience proportions is same.

alternate hyothesis:Ha: viewing audience proportions has changed.

applying chi square goofnes of fit test:

1) from above  test statistic =10.02

2) for(categories-1=4-1=3) degree of freedom ; p value =0.0184

3)as p value is less then 0.05 level we reject null hypothesis

we have sufficient evidence that significant change occurred in viewing audience proportions

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E ABC 0.290 99.000 87.00 1.66 CBS 0.280 76.000 84.00 0.76 NBC 0.250 88.000 75.00 2.25 independent 0.180 37.000 54.00 5.35 1 300 300 10.0223

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