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 95 homes, CBS 70 homes, NBC 89 homes, and independents 46 homes.

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

State the null and alternative hypotheses.

H₀: p_ABC = 0.29, p_CBS = 0.28, p_NBC = 0.25, p_IND = 0.18 H_a: p_ABC ≠ 0.29, p_CBS ≠ 0.28, p_NBC ≠ 0.25, p_IND ≠ 0.18

H₀: The proportions are not p_ABC = 0.29, p_CBS = 0.28, p_NBC = 0.25, p_IND = 0.18.
H_a: p_ABC = 0.29, p_CBS = 0.28, p_NBC = 0.25, p_IND = 0.18    

H₀: p_ABC ≠ 0.29, p_CBS ≠ 0.28, p_NBC ≠ 0.25, p_IND ≠ 0.18
H_a: p_ABC = 0.29, p_CBS = 0.28, p_NBC = 0.25, p_IND = 0.18

H₀: p_ABC = 0.29, p_CBS = 0.28, p_NBC = 0.25, p_IND = 0.18
H_a: The proportions are not p_ABC = 0.29, p_CBS = 0.28, p_NBC = 0.25, p_IND = 0.18.

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 not been a significant change in the viewing audience proportions.

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.

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

Answer 1

H₀: p_ABC = 0.29, p_CBS = 0.28, p_NBC = 0.25, p_IND = 0.18

H_a: The proportions are not p_ABC = 0.29, p_CBS = 0.28, p_NBC = 0.25, p_IND = 0.18

The following table is obtained:

Categories	Observed	Expected	(fo-fe)2/fe
Category 1	95	300*0.29=87	(95-87)2/87 = 0.736
Category 2	70	300*0.28=84	(70-84)2/84 = 2.333
Category 3	89	300*0.25=75	(89-75)2/75 = 2.613
Category 4	46	300*0.18=54	(46-54)2/54 = 1.185
Sum =	300	300	6.867

value of the test statistic. = 6.867

The P-Value is .0763

p value > l.o.s

i.e., 0.0763 > 0.05

so fail to reject H0

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