Controversial Song The song “Baby It’s Cold Outside” generated much controversy because of its lyrics and tone. CBS New York conducted a survey by asking viewers to use the Internet to respond to a question asking whether that song was really too offensive to play. Among 1043 Internet users who chose to respond, 986 said that the song was not too offensive, and 57 of the respondents said that the song was too offensive.


b. Based on the result from part (a), is it safe to say that the majority of the population does not feel that the song is too offensive.

Verified step by step guidance

1. Step 1: Define the problem and identify the statistical concept involved. This problem involves determining whether the majority of the population feels that the song is not too offensive, based on the survey results. This requires analyzing proportions and making inferences about the population based on the sample data.
2. Step 2: Calculate the sample proportion of respondents who said the song is not too offensive. The formula for the sample proportion is: $\frac{x}{n}$, where $x$ is the number of respondents who said the song is not too offensive (986), and $n$ is the total number of respondents (1043).
3. Step 3: Formulate the null and alternative hypotheses for the population proportion. The null hypothesis ($H$₀) is that the population proportion of people who feel the song is not too offensive is less than or equal to 0.5 (no majority). The alternative hypothesis ($H$₁) is that the population proportion is greater than 0.5 (majority).
4. Step 4: Perform a hypothesis test for the population proportion. Use the formula for the test statistic: $\frac{(p-p}{}$₀)p₀(1-p₀)n, where $p$ is the sample proportion, $p$₀ is the hypothesized population proportion (0.5), and $n$ is the sample size.
5. Step 5: Compare the test statistic to the critical value or use the p-value approach to make a decision. If the test statistic exceeds the critical value (or if the p-value is less than the significance level, typically 0.05), reject the null hypothesis and conclude that the majority of the population likely feels the song is not too offensive. Otherwise, fail to reject the null hypothesis.

Key Concepts

Sampling and Population

In statistics, a sample is a subset of a population used to gather insights about the entire group. In this case, the 1,043 Internet users represent a sample from the broader population of all listeners. Understanding the relationship between a sample and its population is crucial for making inferences about general attitudes or opinions based on survey results.

Majority Opinion

A majority opinion refers to the viewpoint held by more than half of a group. In the context of the survey, determining whether the majority of respondents (986 out of 1,043) believe the song is not too offensive is essential for assessing public sentiment. This concept is fundamental in interpreting survey data and making claims about broader societal views.

Statistical Inference

Statistical inference involves drawing conclusions about a population based on sample data. In this scenario, the survey results allow us to infer that a significant portion of the population may not find the song offensive. However, it is important to consider factors such as sample bias and the representativeness of the respondents when making these inferences.