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.

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

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

Answer 1

a) The expected value for each of the 4 categories is computed here as:
E_i = p_i * Total sample size = 300p_i

The computations here are made as:

Category	O_i	E_i	(O_i - E_i)^2/E_i
ABC	93	93	0.0000
CBS	72	78	0.4615
NBC	87	81	0.4444
Independents	48	48	0.0000
	300	300	0.9060

The chi square test statistic is now computed here as: (As seen from the last column)

Therefore 0.906 is the required test statistic value here.

b) For n - 1 = 3 degrees of freedom, the p-value is obtained from the chi square distribution tables as:

Therefore 0.8240 is the required p-value here.