Explanation The null and alternative hypotheses are as follows: Null hypothesis: There is no significant difference in the mean reaction times for the four stimuli. Alternative hypothesis: At least one mean reaction time is different. Here, b = 5 , k = 4 , n = 20 . The sample means are as follows: Y ¯ 1. = ∑ j = 1 n 1 y 1 j n 1 = 0.7 + 0.6 + 0.9 + 0.6 4 = 0.7 Y ¯ 2. = ∑ j = 1 n 2 y 2 j n 2 = 0.8 + 0.6 + 1 + 0.8 4 = 0.8 Y ¯ 3. = ∑ j = 1 n 3 y 3 j n 3 = 1 + 1.1 + 1.2 + 0.9 4 = 1.05 Y ¯ 4. = ∑ j = 1 n 4 y 4 j n 4 = 1 + 1 + 1.1 + 1 4 = 1.025 Y ¯ 5. = ∑ j = 1 n 5 y 5 j n 5 = 0.5 + 0.6 + 0.6 + 0.4 4 = 0.525 Y ¯ = Y ¯ 1. + Y ¯ 2. + Y ¯ 3. + Y ¯ 4. + Y ¯ 5. 5 = 0.82 The total sum of squares is calculated as follows: TSS = ∑ i = 1 4 ∑ j = 1 5 Y i j 2 − 1 20 ( ∑ i = 1 4 ∑ j = 1 5 y i j ) 2 = 14

Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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Chapter 13, Problem 86SE

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Conduct an ANOVA and test for the differences in the mean reaction times for the four stimuli.

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Chapter 13 Solutions

Mathematical Statistics with Applications

Ch. 13.2 - The reaction times for two different stimuli in a...Ch. 13.2 - Prob. 2E Ch. 13.4 - State the assumptions underlying the ANOVA of a...Ch. 13.4 - Prob. 4E Ch. 13.4 - Prob. 5E Ch. 13.4 - Suppose that independent samples of sizes n1, n2,,...Ch. 13.4 - Four chemical plants, producing the same products...Ch. 13.4 - Prob. 8E Ch. 13.4 - Prob. 9E Ch. 13.4 - A clinical psychologist wished to compare three...

Ch. 13.4 - It is believed that women in the postmenopausal...Ch. 13.4 - If vegetables intended for human consumption...Ch. 13.4 - One portion of the research described in a paper...Ch. 13.4 - The Florida Game and Fish Commission desires to...Ch. 13.4 - Prob. 15E Ch. 13.4 - An experiment was conducted to examine the effect...Ch. 13.5 - Prob. 17E Ch. 13.5 - Refer to Exercise 13.17 and consider YiYi for i ...Ch. 13.5 - Refer to the statistical model for the one-way...Ch. 13.7 - Refer to Examples 13.2 and 13.3. a Use the portion...Ch. 13.7 - Refer to Examples 13.2 and 13.4. a Use the portion...Ch. 13.7 - a Based on your answers to Exercises 13.20 and...Ch. 13.7 - Refer to Exercise 13.7. a Construct a 95%...Ch. 13.7 - Prob. 24E Ch. 13.7 - Prob. 25E Ch. 13.7 - Prob. 26E Ch. 13.7 - Prob. 27E Ch. 13.7 - Prob. 28E Ch. 13.7 - Prob. 29E Ch. 13.7 - Prob. 30E Ch. 13.7 - Prob. 31E Ch. 13.7 - Prob. 32E Ch. 13.7 - Prob. 33E Ch. 13.7 - Prob. 34E Ch. 13.7 - Prob. 35E Ch. 13.8 - Prob. 36E Ch. 13.8 - Prob. 37E Ch. 13.8 - Prob. 38E Ch. 13.8 - Prob. 39E Ch. 13.8 - Prob. 40E Ch. 13.9 - Prob. 41E Ch. 13.9 - The accompanying table presents data on yields...Ch. 13.9 - Refer to Exercise 13.42. Why was a randomized...Ch. 13.9 - Prob. 44E Ch. 13.9 - Prob. 45E Ch. 13.9 - Prob. 46E Ch. 13.9 - Prob. 47E Ch. 13.9 - Prob. 48E Ch. 13.9 - Prob. 49E Ch. 13.9 - Prob. 50E Ch. 13.9 - Prob. 51E Ch. 13.10 - Prob. 52E Ch. 13.10 - Prob. 53E Ch. 13.10 - Prob. 54E Ch. 13.10 - Refer to Exercise 13.46. Construct a 95%...Ch. 13.10 - Prob. 56E Ch. 13.10 - Prob. 57E Ch. 13.11 - Prob. 58E Ch. 13.11 - Prob. 59E Ch. 13.11 - Prob. 60E Ch. 13.11 - Prob. 61E Ch. 13.11 - Prob. 62E Ch. 13.12 - Prob. 63E Ch. 13.12 - Prob. 64E Ch. 13.12 - Prob. 65E Ch. 13.12 - Prob. 66E Ch. 13.12 - Prob. 67E Ch. 13.12 - Prob. 68E Ch. 13.13 - Prob. 69E Ch. 13.13 - Prob. 70E Ch. 13.13 - Refer to Exercise 13.42. Answer part (a) by...Ch. 13.13 - Refer to Exercise 13.45. Answer part (b) by...Ch. 13 - Prob. 73SE Ch. 13 - Prob. 74SE Ch. 13 - Prob. 75SE Ch. 13 - Prob. 77SE Ch. 13 - A study was initiated to investigate the effect of...Ch. 13 - Prob. 79SE Ch. 13 - A dealer has in stock three cars (models A, B, and...Ch. 13 - In the hope of attracting more riders, a city...Ch. 13 - Prob. 84SE Ch. 13 - Prob. 85SE Ch. 13 - Prob. 86SE Ch. 13 - Prob. 87SE Ch. 13 - Prob. 88SE Ch. 13 - Prob. 89SE Ch. 13 - Prob. 90SE Ch. 13 - Prob. 92SE Ch. 13 - Prob. 94SE

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Conduct an ANOVA and test for the differences in the mean reaction times for the four stimuli.

Solution Summary: The author concludes that there is no significant difference in the mean reaction times for the four stimuli.

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Conduct an ANOVA and test for the differences in the mean reaction times for the four stimuli.

Chapter 13 Solutions