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 31%, CBS 26%, NBC 27%, and independents 16%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 93 homes, CBS 72 homes, NBC 87 homes, and independents 48 homes.

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

State the null and alternative hypotheses.

H₀: p_ABC = 0.31, p_CBS = 0.26, p_NBC = 0.27, p_IND = 0.16
H_a: The proportions are not p_ABC = 0.31, p_CBS = 0.26, p_NBC = 0.27, p_IND = 0.16.

H₀: p_ABC = 0.31, p_CBS = 0.26, p_NBC = 0.27, p_IND = 0.16
H_a: p_ABC ≠ 0.31, p_CBS ≠ 0.26, p_NBC ≠ 0.27, p_IND ≠ 0.16    

H₀: p_ABC ≠ 0.31, p_CBS ≠ 0.26, p_NBC ≠ 0.27, p_IND ≠ 0.16
H_a: p_ABC = 0.31, p_CBS = 0.26, p_NBC = 0.27, p_IND = 0.16

H₀: The proportions are not p_ABC = 0.31, p_CBS = 0.26, p_NBC = 0.27, p_IND = 0.16.
H_a: p_ABC = 0.31, p_CBS = 0.26, p_NBC = 0.27, p_IND = 0.16

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.

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.    

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.

Answer 1

The statistical software output for this problem is:

From above output:

Hypotheses:

H₀: p_ABC = 0.31, p_CBS = 0.26, p_NBC = 0.27, p_IND = 0.16
H_a: The proportions are not p_ABC = 0.31, p_CBS = 0.26, p_NBC = 0.27, p_IND = 0.16.

Test statistic = 0.906

p - Value = 0.8240

Conclusion:

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

Option B is correct.