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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 9.7
Chapter 9, Problem 9.7

Body Temperatures Listed below are body temperatures from six different subjects measured at two different times in a day (from Data Set 5 “Body Temperatures” in Appendix B).


a. Are the two sets of data independent or dependent? Explain.


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Verified step by step guidance
1
Identify the nature of the data: The problem involves body temperatures measured from the same subjects at two different times in a day.
Understand the concept of dependent and independent data: Dependent data (or paired data) means that the data points are related or paired in some way, such as measurements taken from the same subject at different times. Independent data means that the data points are not related or paired.
Analyze the data collection method: Since the body temperatures are measured from the same subjects at two different times, the data points are paired. This means that each subject's temperature at one time is related to their temperature at another time.
Conclude the relationship: Based on the analysis, the two sets of data are dependent because they involve repeated measurements from the same subjects.
Explain the implication: Understanding that the data is dependent is crucial for choosing the correct statistical test for analysis, such as a paired t-test, which is used for comparing two related samples.

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Key Concepts

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

Independent vs. Dependent Samples

Independent samples are those where the observations in one sample do not affect or relate to the observations in another. Dependent samples, also known as paired samples, involve observations that are related or matched in some way, such as measurements taken from the same subjects at different times. In this context, since the body temperatures are measured from the same subjects at two different times, the data sets are dependent.
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Paired Sample Analysis

Paired sample analysis is used when comparing two related samples, such as measurements taken from the same subjects under different conditions. This analysis accounts for the natural pairing of the data, allowing for more accurate comparisons by considering the differences within each pair. In the given question, since the body temperatures are measured from the same individuals at two different times, a paired sample analysis would be appropriate.
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Repeated Measures Design

A repeated measures design involves collecting multiple measurements from the same subjects over time or under different conditions. This design helps control for individual variability, as each subject serves as their own control. In the context of the question, the body temperatures are measured at two different times for the same subjects, indicating a repeated measures design, which is crucial for understanding the dependency between the data sets.
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Related Practice
Textbook Question

No Variation in a Sample An experiment was conducted to test the effects of alcohol. Researchers measured the breath alcohol levels for a treatment group of people who drank ethanol and another group given a placebo. The results are given below (based on data from “Effects of Alcohol Intoxication on Risk Taking, Strategy, and Error Rate in Visuomotor Performance,” by Streufert et al., Journal of Applied Psychology, Vol. 77, No. 4). Use a 0.05 significance level to test the claim that the two sample groups come from populations with the same mean.


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Textbook Question

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.


Exercise 8 in Section 9-1 “Tennis Challenges”


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Textbook Question

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.


Exercise 9 in Section 9-1 “Cell Phones and Handedness”


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Textbook Question

Degrees of Freedom For Example 1, we used df=smaller of n1-1 and n2-1 we got df=11 and the corresponding critical value is t=-1.796 (found from Table A-4). If we calculate df using Formula 9-1, we get df=19.370 and the corresponding critical value is t=-1.727 How is using the critical value of t=-1.796 “more conservative” than using the critical value of t=-1.727

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Textbook Question

Is Friday the 13th Unlucky? Listed below are numbers of hospital admissions in one region due to traffic accidents on different Fridays falling on the 6th day of a month and the following 13th day of the month (based on data from “Is Friday the 13th Bad for Your Health,” by Scanlon et al., British Medical Journal, Vol. 307). Assume that we want to use a 0.05 significance level to test the claim that the data support the claim that fewer hospital admissions due to traffic accidents occur on Friday the 6th than on the following Friday the 13th. Identify the null hypothesis and alternative hypothesis.


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Textbook Question

Degrees of Freedom In Exercise 20 “Blanking Out on Tests,” using the “smaller of n1-1 and n2-1” for the number of degrees of freedom results in df=15 Find the number of degrees of freedom using Formula 9-1. In general, how are hypothesis tests and confidence intervals affected by using Formula 9-1 instead of the “smaller of n1-1 and n2-1 ”?

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