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Ch. 7 - Estimating Parameters and Determining Sample Sizes
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 7 - Estimating Parameters and Determining Sample SizesProblem 7.CR.8b
Chapter 7, Problem 7.CR.8b

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.

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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.
Step 2: Calculate the sample proportion of respondents who said the song is not too offensive. The formula for the sample proportion is: xn, 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).
Step 3: Formulate the null and alternative hypotheses for the population proportion. The null hypothesis (H0) 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 (H1) is that the population proportion is greater than 0.5 (majority).
Step 4: Perform a hypothesis test for the population proportion. Use the formula for the test statistic: (p-p0)p0(1-p0)n, where p is the sample proportion, p0 is the hypothesized population proportion (0.5), and n is the sample size.
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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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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.
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Related Practice
Textbook Question

Space Mountain Use the following wait times (minutes) for the Space Mountain ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B). Construct a 95% confidence interval estimate of the mean of all wait times. Write a brief statement that interprets that confidence interval.


40 35 40 40 25 80 50 30 35 40

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Textbook Question

Distributions Identify the distribution (normal, Student t, chi-square) that should be used in each of the following situations. If none of the three distributions can be used, what other method could be used?


a. In constructing a confidence interval of , you have 75 sample values and they appear to be from a population with a skewed distribution. The population standard deviation is not known.


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Textbook Question

Arm Circumferences Listed below are arm circumferences (cm) of randomly selected women (based on Data Set 1 “Body Data” from Appendix B). Also shown is the normal quantile plot of those measurements.


b. Are the requirements for constructing a 95% confidence interval estimate of the population standard deviation satisfied? If so, construct that confidence interval.

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Textbook Question

Requirements A construction quality control analyst has collected a random sample of six concrete road barriers, and she plans to weigh each of them and construct a 95% confidence interval estimate of the mean weight of all such barriers. What requirements must be satisfied in order to construct the confidence interval with the method from Section 7-2 that uses the t distribution?

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Textbook Question

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.

.

c. What is wrong with this survey? Based on this survey, what do we really know about the population?

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Textbook Question

Degrees of Freedom In general, what does “degrees of freedom” refer to? For the sample data described in Exercise 7 “Requirements,” find the number of degrees of freedom, assuming that you want to construct a confidence interval estimate of u using the t distribution.

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