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 30%, CBS 27%, NBC 26%, and independents 17%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 96 homes, CBS 69 homes, NBC 90 homes, and independents 45 homes.

Test with α = 0.05 to determine whether the viewing audience proportions changed.

State the null and alternative hypotheses.

H₀: p_ABC ≠ 0.30, p_CBS ≠ 0.27, p_NBC ≠ 0.26, p_IND ≠ 0.17
H_a: p_ABC = 0.30, p_CBS = 0.27, p_NBC = 0.26, p_IND = 0.17 H₀: p_ABC = 0.30, p_CBS = 0.27, p_NBC = 0.26, p_IND = 0.17
H_a: p_ABC ≠ 0.30, p_CBS ≠ 0.27, p_NBC ≠ 0.26, p_IND ≠ 0.17     H₀: The proportions are not p_ABC = 0.30, p_CBS = 0.27, p_NBC = 0.26, p_IND = 0.17.
H_a: p_ABC = 0.30, p_CBS = 0.27, p_NBC = 0.26, p_IND = 0.17 H₀: p_ABC = 0.30, p_CBS = 0.27, p_NBC = 0.26, p_IND = 0.17
H_a: The proportions are not p_ABC = 0.30, p_CBS = 0.27, p_NBC = 0.26, p_IND = 0.17.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. There has been a significant change in the viewing audience proportions. Reject H₀. There has not been a significant change in the viewing audience proportions.      Do not reject H₀. There has been a significant change in the viewing audience proportions. Do not reject H₀. There has not been a significant change in the viewing audience proportions.

Answer 1

*** Null and alternative hypotheses:

H0: pABC = 0.30, pCBS = 0.27, pNBC = 0.26, pIND = 0.17
Ha: The proportions are not pABC = 0.30, pCBS = 0.27, pNBC = 0.26, pIND = 0.17

*** Conclusion: Do not reject H0. There has not been a significant change in the viewing audience proportions.

(The above conclusion holds as the p-value is greater than the significance level of 0.05)