Question

During the first 13 weeks of the television seoson, the Saturdwy evening .8:00 FH. to 9:00 p.M. audience propertions were recorded as ABC 30%:, CBS 27%, NBC 24%, and independents 195. A sample of 300 homes two weeks after a Saturdoy night schedule revislon yielded the following viening audience data: ABC 92 homes, CaS 64 homes, NBC 86 homes, and Independents 5S homes. Test with α=0.05 to determine whether the viewing audience proportions changed Find the test statistic and p-value

Answer 1

To test whether the viewing audience proportions changed, we can use a chi-squared goodness-of-fit test.

Step-by-step explanation:

To test whether the viewing audience proportions changed, we can use a chi-squared goodness-of-fit test. First, we need to calculate the expected frequencies for each network based on the null hypothesis that there is no change. The expected frequency for each network can be calculated by multiplying the overall proportion of viewers (sample size/total population) by the total sample size.

Next, we can calculate the chi-square test statistic by summing the squared differences between the observed and expected frequencies, divided by the expected frequencies.

Finally, we can find the p-value associated with the test statistic using the chi-square distribution with (k - 1) degrees of freedom, where k is the number of categories. We can compare this p-value to the significance level (α) to determine if there is sufficient evidence to reject the null hypothesis.