Question

During the first few weeks of the new television season, the evening news audience proportions were recorded as: ABC = 31 5, CBS = 34%, NBC = 35%. A sample of 600 homes yielded the following viewing audience data. Channel Number of Homes ABC 150 CBS 200 NBC 250 We want to determine whether or not there has been a significant change in the percentage of viewing audience of the three networks. Conduct the appropriate hypothesis test at an alpha level of .01.

Answer 1

Solution:

Given: During the first few weeks of the new television season, the evening news audience proportions were recorded as:

ABC = 31%,

CBS = 34%,

NBC = 35%.

Sample size = N =600

Channel Number of Homes

ABC      : 150

CBS      : 200

NBC    : 250

We have to test whether or not there has been a significant change in the percentage of viewing audience of the three networks.

Level of significance = 0.01

Step 1) State H0 and H1:

H0: there has not been a significant change in the percentage of viewing audience of the three networks.

Vs

H1: there has been a significant change in the percentage of viewing audience of the three networks.

Step 2) Find test statistic:

We use Chi-square test statistic:

Where

O_i = Observed Counts

E_i =Expected Counts

Thus we need to make following table:

Channel	Oi	Expected Proportions	Ei	Oi2/Ei
ABC	150	31%	186	120.968
CBS	200	34%	204	196.078
NBC	250	35%	210	297.619
	N =600

To get Ei, we multiply each Expected Proportions by N =600.

Thus we get:

Step 3) Find Chi-square critical value:

df = k - 1 = 3 - 1 = 2

Level of significance = 0.01

Chi-square critical value = 9.210

Step 4) Decision Rule:

Reject H0, if Chi-square test statistic value > Chi-square critical value = 9.210, otherwise we fail to reject H0.

Since Chi-square test statistic value = > Chi-square critical value = 9.210, we reject H0.

Step 5) Conclusion:

Since we have rejected H0, there has been a significant change in the percentage of viewing audience of the three networks