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Ch. 9 - Inferences from Two Samples
Triola - Elementary Statistics 14th Edition
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Tutti i libri di testoTriola 14th EditionCh. 9 - Inferences from Two SamplesProblema 3
Capitolo 9, Problema 3

Randomization with Commute Times Given the two samples of commute times (minutes) shown here, which of the following are randomizations of them?


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a. Boston: 10 10 60. New York: 5 20 25 30 45.
b. Boston: 10 10 60 20 25. New York: 5 30 45.
c. Boston: 5 10 25 25 60. New York: 5 30 30 60.
d. Boston: 10 10 60. New York: 5 20 25 30 45.
e. Boston: 10 10 10 10 10. New York: 60 60 60.

Guida verificata passo dopo passo
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Step 1: Understand the concept of randomization. Randomization involves rearranging or redistributing the data points between groups while maintaining the total number of data points in each group. This process ensures that the groups are formed randomly without any inherent bias.
Step 2: Analyze the original samples provided. The original commute times are: Boston: 10, 10, 60 and New York: 5, 20, 25, 30, 45. These are the baseline distributions of commute times for the two cities.
Step 3: Evaluate each option to determine if it represents a valid randomization. For a valid randomization, the total number of data points in each group must remain consistent with the original sample sizes (Boston: 3 data points, New York: 5 data points), and the data points must be redistributed randomly between the groups.
Step 4: Check for duplicates or patterns that might indicate non-randomization. For example, in option (e), Boston has all identical values (10, 10, 10, 10, 10), and New York has all identical values (60, 60, 60). This is not a randomization but rather a systematic grouping.
Step 5: Compare each option to the original samples and verify whether the redistribution of data points adheres to the principles of randomization. Ensure that the total number of data points and the original values are preserved in the new groupings.

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Randomization

Randomization is a statistical technique used to assign individuals or items to different groups in a way that eliminates bias. In the context of comparing two samples, randomization ensures that the samples are representative of the population, allowing for valid conclusions about differences or similarities. It is crucial for ensuring that the results of an analysis are not influenced by external factors.
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Intro to Random Variables & Probability Distributions

Sample Size and Composition

Sample size refers to the number of observations or data points collected in a study. The composition of a sample, including its distribution and range of values, affects the reliability of statistical analyses. In the given question, understanding the sample sizes and their respective values is essential to determine if the proposed randomizations maintain the integrity of the original samples.
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Sampling Distribution of Sample Proportion

Statistical Validity

Statistical validity refers to the extent to which the conclusions drawn from a statistical analysis are accurate and applicable to the real world. This includes ensuring that the samples used are appropriate for the analysis being conducted. In the context of the question, assessing whether the proposed randomizations preserve the original sample characteristics is key to determining their validity.
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Finding Critical Values

In Exercises 17–20, refer to the information in the given exercise and use a 0.05 significance level for the following.


a. Find the critical value(s).

b. Should we reject H0 or should we fail to reject H0?


Exercise 14

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Color and Recall Researchers from the University of British Columbia conducted trials to investigate the effects of color on the accuracy of recall. Subjects were given tasks consisting of words displayed on a computer screen with background colors of red and blue. The subjects studied 36 words for 2 minutes, and then they were asked to recall as many of the words as they could after waiting 20 minutes. Results from scores on the word recall test are given below. Use a 0.05 significance level to test the claim that variation of scores is the same with the red background and blue background.


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Smoking Cessation Programs


b. Does the difference between the success rate of the sustained care program and the standard care program appear to have practical significance?


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