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Ch. 9 - Inferences from Two Samples
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 9 - Inferences from Two SamplesProblem 9.2.1a
Chapter 9, Problem 9.2.1a

Independent Samples Which of the following involve independent samples?


a. Data Set 4 “Measured and Reported” includes measured heights matched with the heights that were reported when the subjects were asked for those values.

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Step 1: Understand the concept of independent samples. Independent samples are those where the observations in one sample do not influence or are not related to the observations in another sample. Each sample is collected separately and does not depend on the other.
Step 2: Analyze the given data set. In this case, 'Measured and Reported' includes measured heights matched with reported heights. This indicates that each measured height is paired with a corresponding reported height for the same subject.
Step 3: Determine whether the samples are independent or dependent. Since the measured heights are matched with the reported heights for the same individuals, the two sets of data are related. This means the samples are dependent, not independent.
Step 4: Clarify the distinction between dependent and independent samples. Dependent samples involve paired or matched data, where one sample is directly related to the other. Independent samples, on the other hand, involve separate groups with no pairing or relationship between the samples.
Step 5: Conclude that the example provided does not involve independent samples because the measured and reported heights are matched for the same subjects, making them dependent samples.

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Key Concepts

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

Independent Samples

Independent samples refer to groups of data that are collected from different subjects or entities, where the selection of one sample does not influence the selection of another. This concept is crucial in statistical testing, as it allows for comparisons between groups without the risk of bias or confounding variables that could arise from related samples.
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Sampling Distribution of Sample Proportion

Matched Samples

Matched samples involve pairs of observations that are related or linked in some way, often used to control for variables that could affect the outcome. In the context of the question, the measured heights and reported heights are matched because they come from the same subjects, making them dependent rather than independent samples.
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Sampling Distribution of Sample Proportion

Statistical Testing

Statistical testing is a method used to determine if there is a significant difference between groups or conditions. Understanding whether samples are independent or dependent is essential for selecting the appropriate statistical test, such as t-tests for independent samples or paired t-tests for matched samples, which can yield different results based on the sample structure.
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Guided course
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Step 2: Calculate Test Statistic
Related Practice
Textbook Question

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1-1 and n2-1)


Color and Cognition Researchers from the University of British Columbia conducted a study to investigate the effects of color on cognitive tasks. Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below. Higher scores correspond to greater word recall.


a. Use a 0.05 significance level to test the claim that the samples are from populations with the same mean.


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Textbook Question

Are Seat Belts Effective? A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed (based on data from “Who Wants Airbags?” by Meyer and Finney, Chance, Vol. 18, No. 2). We want to use a 0.05 significance level to test the claim that seat belts are effective in reducing fatalities.


a. Test the claim using a hypothesis test.

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Textbook Question

Hypotheses and Conclusions Refer to the hypothesis test described in Exercise 1.


a. Identify the null hypothesis and the alternative hypothesis.


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Textbook Question

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1-1 and n2-1)


Color and Creativity Researchers from the University of British Columbia conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given below. Higher scores correspond to more creativity. The researchers make the claim that “blue enhances performance on a creative task.”


a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task.


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Textbook Question

Confidence Interval Assume that we want to use the sample data in Exercise 1 for constructing a confidence interval to be used for testing the given claim.


a. What is the confidence level that should be used for the confidence interval?


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Textbook Question

Count Five Test for Comparing Variation in Two Populations Repeat Exercise 16 “Blanking Out on Tests,” but instead of using the F test, use the following procedure for the “count five” test of equal variations (which is not as complicated as it might appear).

a. For each value x in the first sample, find the absolute deviation |x-x_bar| then sort the absolute deviation values. Do the same for the second sample.

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