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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 8
Chapter 9, Problem 8

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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Verified step by step guidance
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Step 1: Identify the hypothesis test to be used. Since the problem involves comparing the variation (or variance) of two groups (red background and blue background), we will use an F-test for equality of variances.
Step 2: State the null and alternative hypotheses. The null hypothesis (H₀) is that the variances of the two groups are equal (σ₁² = σ₂²). The alternative hypothesis (H₁) is that the variances are not equal (σ₁² ≠ σ₂²).
Step 3: Calculate the test statistic. The F-test statistic is calculated as the ratio of the larger sample variance to the smaller sample variance: F = s₁² / s₂², where s₁² and s₂² are the sample variances of the two groups. Ensure you identify which group has the larger variance.
Step 4: Determine the critical value or p-value. Use the F-distribution table or statistical software to find the critical value for the F-test at a significance level of 0.05. The degrees of freedom for the numerator (df₁) and denominator (df₂) are based on the sample sizes of the two groups (df₁ = n₁ - 1, df₂ = n₂ - 1).
Step 5: Make a decision. Compare the calculated F-test statistic to the critical value. If the test statistic exceeds the critical value, reject the null hypothesis. Alternatively, if using the p-value approach, reject the null hypothesis if the p-value is less than 0.05. Interpret the results in the context of the problem.

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Key Concepts

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

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) that represents no effect or no difference, and an alternative hypothesis (H1) that indicates the presence of an effect or difference. Researchers use significance levels, such as 0.05, to determine whether to reject the null hypothesis based on the p-value obtained from the data.
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Step 1: Write Hypotheses

Variance and Standard Deviation

Variance measures the dispersion of a set of data points around their mean, indicating how much the scores vary. Standard deviation, the square root of variance, provides a more interpretable measure of spread in the same units as the data. In the context of the study, comparing the variances of recall scores for different background colors helps assess whether the color affects recall accuracy.
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Calculating Standard Deviation

ANOVA (Analysis of Variance)

ANOVA is a statistical technique used to compare the means of three or more groups to determine if at least one group mean is significantly different from the others. In this case, it can be applied to test if the variation in recall scores differs significantly between the red and blue backgrounds. ANOVA helps in understanding the impact of categorical independent variables on a continuous dependent variable.
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Variance & Standard Deviation of Discrete Random Variables
Related Practice
Textbook Question

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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Textbook Question

Testing Effects of Alcohol Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 22 people who drank ethanol and another group of 22 people given a placebo. The errors for the treatment group have a standard deviation of 2.20, and the errors for the placebo group have a standard deviation of 0.72 (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 both groups have the same amount of variation among the errors.

Textbook Question

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.

Textbook Question

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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Textbook Question

In Exercises 17–24, use the indicated Data Sets from Appendix B. The complete data sets can be found at www.TriolaStats.com. Assume that the paired sample data are simple random samples and the differences have a distribution that is approximately normal.

Measured and Reported Weights Repeat Example 1 using all of the 2784 measured and reported weights of males listed in Data Set 4 “Measured and Reported” in Appendix B. Did the larger data set have much of an effect on the results?