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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 9.2.1c
Chapter 9, Problem 9.2.1c

Independent Samples Which of the following involve independent samples?


c. Data Set 1 “Body Data” includes a sample of pulse rates of 147 women and a sample of pulse rates of 153 men.

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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 depend on the observations in another sample. This is a key distinction from dependent samples, where there is a relationship or pairing between the samples.
Step 2: Analyze the given data. In this problem, we are provided with two separate samples: one consisting of pulse rates of 147 women and another consisting of pulse rates of 153 men.
Step 3: Evaluate whether the samples are independent. Since the pulse rates of women and men are measured separately and there is no indication that the pulse rates of individuals in one group affect or are related to the pulse rates of individuals in the other group, the samples can be considered independent.
Step 4: Consider the context of the problem. If there is no pairing or matching between the individuals in the two groups (e.g., no husband-wife pairs or other relationships), this further supports the conclusion that the samples are independent.
Step 5: Conclude that the two samples (pulse rates of women and pulse rates of men) are independent based on the lack of any dependency or relationship between the observations in the two groups.

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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 collected from different populations 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 affecting the results.
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Sampling Distribution of Sample Proportion

Sampling Methodology

Sampling methodology involves the techniques used to select individuals or items from a population to form a sample. Understanding different sampling methods, such as random sampling or stratified sampling, is essential for ensuring that the samples are representative and that the results can be generalized to the larger population.
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Sampling Distribution of Sample Proportion

Statistical Tests for Independent Samples

Statistical tests for independent samples, such as the t-test, are used to determine if there are significant differences between the means of two independent groups. These tests assume that the samples are drawn from normally distributed populations and that they have equal variances, making it important to verify these assumptions before conducting the analysis.
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Step 2: Calculate Test Statistic
Related Practice
Textbook Question

Overlap of Confidence Intervals In the article “On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals,” by Schenker and Gentleman (American Statistician, Vol. 55, No. 3), the authors consider sample data in this statement: “Independent simple random samples, each of size 200, have been drawn, and 112 people in the first sample have the attribute, whereas 88 people in the second sample have the attribute.”


c. Use a 0.05 significance level to test the claim that the two population proportions are equal. What do you conclude?


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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)


Magnet Treatment of Pain People spend around \$5 billion annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the results obtained in the study (based on data from “Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study,” by Collacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 283, No. 10). Higher scores correspond to greater pain levels.


c. Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?


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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.


c. What does the result suggest about the effectiveness of seat belts?

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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).

c. If the sample sizes are equal (n1 = n2) use a critical value of 5. If n1 is not equals to n2 calculate the critical value shown below.

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Textbook Question

In Exercises 5–16, use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal.


The Freshman 15 The “Freshman 15” refers to the belief that college students gain 15 lb (or 6.8 kg) during their freshman year. Listed below are weights (kg) of randomly selected male college freshmen (from Data Set 13 “Freshman 15” in Appendix B). The weights were measured in September and later in April.


c. What do you conclude about the Freshman 15 belief?


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Textbook Question

Clinical Trials of OxyContin OxyContin (oxycodone) is a drug used to treat pain, but it is well known for its addictiveness and danger. In a clinical trial, among subjects treated with OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjects given placebos, 5 developed nausea and 40 did not develop nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test for a difference between the rates of nausea for those treated with OxyContin and those given a placebo.


c. Does nausea appear to be an adverse reaction resulting from OxyContin?

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