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 26%, NBC 22%, and independents 22%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 91 homes, CBS 68 homes, NBC 83 homes, and independents 58 homes. Test with to determine whether the viewing audience proportions changed.Compute the value of the test statistic (to 2 decimals).

Answer 1

The value of the test statistic is 6.642.

Explanation:

A Chi-square test for Goodness of fit will be used to determine whether the viewing audience proportions changed.

The hypothesis is defined as:

H₀: The viewing audience proportions has not changed.

Hₐ: The viewing audience proportions has changed.

The test statistic is:

`\chi^(2)=\sum ((O-E)^(2))/(E)`

Here,

O = observed frequencies (O - E)²

E = expected frequencies = n × p

The table below shows the observed and expected frequencies.

Compute the test statistic value as follows:

`\chi^(2)=\sum ((O-E)^(2))/(E)\\=0.011+1.282+4.379+0.970\\=6.642`

Thus, the value of the test statistic is 6.642.