Are The TV Habits Of Americans Changing In 2015?

Are The Tv Habits Of Americans Changing In 2015 The Bureau Of Labor

Are the TV habits of Americans changing? In 2015, the Bureau of Labor Statistics found the average number of TV hours watched per day was 4.8. In 2017, the Nielsen rating company conducted a survey and computed the following 95% confidence interval: (3.54, 4.66).

(a) What should Nielsen conclude for α = 0.05? There is --- insufficient sufficient evidence to conclude the average number of TV hours watched per day has --- changed stayed the same.

(b) Nielsen considers making 90% and 99% confidence intervals for their test results. For which of these intervals could they claim the average number of TV hours watched per day has changed? (Choose TWO answers below.)

- For the 90% interval: without actually computing the interval, it can't be known if they could conclude the average number of TV hours watched per day has changed.

- For the 90% interval: they could conclude the average number of TV hours watched per day has changed without even computing it.

- For the 99% interval: without actually computing the interval, it can't be known if they could conclude the average number of TV hours watched per day has changed.

- For the 99% interval: they could conclude the average number of TV hours watched per day has changed without even computing it.

Paper For Above instruction

The investigation into the changing television habits of Americans involves statistical analysis based on survey data collected by different organizations at different times. The core question centers around whether there has been a significant change in the average number of hours Americans watch TV daily over a given period, specifically between 2015 and 2017.

Initially, in 2015, the Bureau of Labor Statistics (BLS) reported that Americans watched an average of 4.8 hours of television per day. This figure established a baseline measure for American TV consumption at that time. Subsequently, in 2017, Nielsen, a well-known market research firm specializing in audience measurement, conducted a survey resulting in a 95% confidence interval of (3.54, 4.66) hours for the average daily TV viewing time.

The critical statistical question revolves around whether the interval provided by Nielsen suggests a significant change from the 2015 baseline. To assess this, we examine if the interval (3.54, 4.66) includes the 2015 value of 4.8 hours. Since 4.8 is greater than the upper limit of the interval, which is 4.66, this indicates that the interval does not contain the previous average of 4.8 hours. From this, we infer that at a 5% significance level (α = 0.05), there is sufficient evidence to conclude that the average TV watching time has changed over this period.

Specifically, because the entire 95% confidence interval is below the 2015 mean, Nielsen can conclude with statistical significance that the average hours of television watched per day has decreased. This deduction fits the hypothesis testing framework, where the null hypothesis states there has been no change in the average, and the alternative hypothesis indicates that a change has occurred.

Turning to the broader context of confidence intervals at different levels, Nielsen also considers constructing 90% and 99% intervals for the same data. The size of the confidence interval increases or decreases depending on the confidence level; a higher confidence level (e.g., 99%) results in a wider interval, while a lower level (e.g., 90%) produces a narrower one.

For the 90% confidence interval, since it is narrower than the 95% interval, it is less likely to include the previous mean (4.8). If the 90% interval does not include 4.8, then the evidence supports the conclusion that the average TV viewing time has changed. Conversely, if the 90% interval were to include 4.8, then there would be insufficient evidence at that confidence level to declare a change.

For the 99% confidence interval, which is wider than the 95% interval, the probability of it including the previous mean (4.8) is higher. If this 99% interval does include 4.8, then at the 1% significance level, we cannot reject the null hypothesis of no change. Still, if it does not include 4.8, then we can infer a significant change.

Given the original 95% interval (3.54, 4.66), which does not contain 4.8, it suggests that the true mean has likely decreased, and the finding remains consistent across different confidence intervals. Therefore, the two correct conclusions are:

- The 90% confidence interval, being narrower, might still exclude 4.8 if the true change is significant, supporting the claim that TV habits have shifted. If it does not include 4.8, then Nielsen could claim a change without further computation.

- The 99% confidence interval, being wider, more reliably excludes 4.8, reinforcing the conclusion that the average TV watching time has changed.

In summary, Nielsen's analysis indicates a significant decrease in the average daily TV viewing hours between 2015 and 2017. The evidence derived from the confidence interval supports the conclusion that Americans are watching less TV, reflecting shifting media consumption habits possibly influenced by the rise of digital devices and streaming services.

References

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