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Ch. 8 - Hypothesis Testing with Two Samples
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 8 - Hypothesis Testing with Two SamplesProblem 8.1.5
Chapter 8, Problem 8.1.5

Independent and Dependent Samples In Exercises 5–8, classify the two samples as independent or dependent and justify your answer.
Sample 1: The maximum bench press weights for 53 football players
Sample 2: The maximum bench press weights for the same 53 football players after completing a weight lifting program

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1
Identify the two samples provided in the problem: Sample 1 consists of the maximum bench press weights for 53 football players, and Sample 2 consists of the maximum bench press weights for the same 53 football players after completing a weight lifting program.
Understand the relationship between the two samples. Since the same individuals (the 53 football players) are measured before and after the weight lifting program, the samples are not independent of each other.
Define dependent samples: Dependent samples (also called paired or matched samples) occur when the data in one sample is directly related to the data in the other sample, such as measurements taken on the same subjects at different times.
Justify the classification: In this case, the two samples are dependent because each football player's bench press weight in Sample 1 is paired with their bench press weight in Sample 2, and the comparison is based on the same individuals.
Conclude that the two samples are dependent and explain that this classification is important because it determines the type of statistical test or analysis that should be used to compare the two samples (e.g., a paired t-test for 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 two or more groups that are not related or paired in any way. In statistical analysis, this means that the selection or outcome of one sample does not influence the other. For example, if you were comparing the test scores of two different classes, the scores from one class would be independent of the scores from the other.
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Dependent Samples

Dependent samples, also known as paired samples, involve groups that are related or matched in some way. This typically occurs when the same subjects are measured under different conditions or at different times. An example is measuring the weight of individuals before and after a diet program, where the same individuals are involved in both measurements.
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Justification in Statistical Analysis

Justification in statistical analysis involves providing reasoning for classifying samples as independent or dependent based on their relationship. This is crucial for selecting the appropriate statistical tests, as the choice between tests for independent or dependent samples can significantly affect the results and interpretations. Clear justification helps ensure the validity of the conclusions drawn from the data.
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Related Practice
Textbook Question

Testing a Difference Other Than Zero Sometimes a researcher is interested in testing a difference in means other than zero. In Exercises 27 and 28, you will test the difference between two means using a null hypothesis of Ho: μ1-μ2=k, Ho: μ1-μ2>=k or Ho: μ1-μ2<=k . The standardized test statistic is still

Architect Salaries Is the difference between the mean annual salaries of entry level architects in Denver, Colorado, and Lincoln, Nebraska, equal to \(9000? To decide, you select a random sample of entry level architects from each city. The results of each survey are shown in the figure. Assume the population standard deviations are σ1=\)6560 and σ2=\$6100 . At α=0.01 what should you conclude? (Adapted from Salary.com)

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Textbook Question

In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions and at the level of significance . Assume the samples are random and independent.


Claim: p1≠p2, α=0.01


Sample statistics: x1=35, n1=70, and x2=36, n2=60

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Textbook Question

Constructing Confidence Intervals for μd To construct a confidence interval for μd , use the inequality below.

Construct the indicated confidence interval for μd . Assume the populations are normally distributed.

[APPLET] Drug Testing A sleep disorder specialist wants to test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the night. To do so, the specialist randomly selects 16 patients and records the number of hours of sleep each gets with and without the new drug. The table shows the results of the two-night study. Construct a 90% confidence interval for μd.

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Textbook Question

Test the claim about the difference between two population means and at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ1=μ2, α=0.01, Assume (σ1)^2=(σ2)^2

Sample statistics:

x̅1=33.7, s1=3.5 , n1=12 and x̅2=35.5 , s2=2.2 , n2=17

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Textbook Question

Constructing Confidence Intervals for μ1-μ2. When the sampling distribution for x̅1-x̅2 is approximated by a t-distribution and the populations have equal variances, you can construct a confidence interval for μ1-μ2, as shown below.

Construct the indicated confidence interval for μ1-μ2 . Assume the populations are approximately normal with equal variances.

Family Doctor 

To compare the mean number of days spent waiting to see a family doctor for two large cities, you randomly select several people in each city who have had an appointment with a family doctor. The results are shown at the left. Construct a 90% confidence interval for the difference in mean number of days spent waiting to see a family doctor for the two cities. (Adapted from Merritt Hawkins)

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Textbook Question

Parks and Mental Health In Exercises 13–18, use the figure, which shows the percentages from a survey of two hundred 18- to 24-year-olds in the United States who say that various park and recreation activities have a positive impact on their mental health. (Adapted from National Recreation and Park Association)



Exercising and Taking Classes At α=0.01, can you reject the claim that the proportion of 18- to 24-year-olds who benefit mentally from exercising in parks is greater than or equal to the proportion who benefit mentally from taking classes in parks?

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