Question

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 90 homes, CBS 77 homes, NBC 83 homes, and independents 50 homes. Test with α = 0.05 to determine whether the viewing audience proportions changed. Compute the value of the test statistic (to 2 decimals).

Answer 1

Explanation:

Given that 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%

H0: Proportion did not change

Ha: Proportions changed

5% significance level is used

ABC CBS NBC INDEP TOTAL

percent 29 28 25 18 100

OBSERVED 90 77 83 50 300

Expected 87 84 75 54 300

chi square 0.103448276 0.583333333 0.853333333 0.296296296 1.836411239

df 3

p value 0.6071

Since p > alpha, we accept null hypothesis

The observed values are as per the proportions.