AOL Time Warner Inc.'s CNN has been the longtime ratings...

AOL Time Warner Inc.'s CNN has been the longtime ratings leader of cable television news. Nielsen Media Research indicated that the mean $\mathrm{CNN}$ viewing audience was 600,000 viewers per day during 2002 (The Wall Street Joumal, March 10, 2003). Assume that for a sample of 40 days during the first half of 2003 , the daily audience was 612,000 viewers with a sample standard deviation of 65,000 viewers. a. What are the hypotheses if CNN management would like information on any change in the $\mathrm{CNN}$ viewing audience? b. What is the $p$-value? c. Select your own level of significance. What is your conclusion? d. What recommendation would you make to $\mathrm{CNN}$ management in this application?

AOL Time Warner Inc.'s CNN has been the longtime ratings leader of cable television news. Nielsen Media Research indicated that the mean $\mathrm{CNN}$ viewing audience was 600,000 viewers per day during 2002 (The Wall Street Joumal, March 10, 2003). Assume that for a sample of 40 days during the first half of 2003 , the daily audience was 612,000 viewers with a sample standard deviation of 65,000 viewers.
a. What are the hypotheses if CNN management would like information on any change in the $\mathrm{CNN}$ viewing audience?
b. What is the $p$-value?
c. Select your own level of significance. What is your conclusion?
d. What recommendation would you make to $\mathrm{CNN}$ management in this application?

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical process used to assess the evidence provided by a sample of data about a population parameter. It involves establishing a null hypothesis (usually denoting no effect or status quo) and an alternative hypothesis (indicating a deviation or effect), and then using sample data to determine whether the evidence is strong enough to reject the null hypothesis in favor of the alternative.

Null and Alternative Hypotheses

The null hypothesis (H0) states that there is no change or no difference from the expected value, while the alternative hypothesis (Ha) represents the possibility of a change or difference. In a two-tailed test, the alternative hypothesis considers deviations in both directions, allowing for the possibility that the parameter could be either higher or lower than the hypothesized value.

p-value

The p-value is the probability, assuming the null hypothesis is true, of observing a test statistic at least as extreme as the one derived from the sample data. A small p-value indicates that such an extreme result is unlikely under the null hypothesis, providing evidence against it, whereas a large p-value suggests that the observed data are consistent with the null hypothesis.

Significance Level

The significance level, often denoted by ?, is a predetermined threshold used to decide whether the observed effect in the sample is statistically significant. It represents the probability of rejecting the null hypothesis when it is actually true (a Type I error). Commonly used significance levels are 0.05 or 0.01.

t-Distribution and One-Sample t-Test

When the sample size is small or the population standard deviation is unknown, the t-distribution is used instead of the normal distribution. The one-sample t-test specifically compares the sample mean to a known value (or hypothesized population mean), taking into account the variability in the sample through the sample standard deviation, and calculates a test statistic that follows a t-distribution with n-1 degrees of freedom.

Statistical Conclusion and Recommendations

Drawing conclusions from a hypothesis test involves comparing the p-value to the significance level. If the p-value is less than the significance level, the null hypothesis is rejected, suggesting evidence of a change or effect. Statistical conclusions, along with practical considerations such as the implications of errors and the real-world context, inform the recommendations made based on the test results.

Transcript

Please give Ace some feedback