Opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students’ test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later. The students receive the following arithmetic test scores: Water Coffee Espresso Caffeine Content (mg/oz) 0 13.4 51.3 78 92 83 ΣX² = 142,493 88 87 83 G = 1,723 72 80 76 N = 21 72 89 79 k = 3 64 96 86 81 83 79 82 92 81 T₁ = 537 T₂ = 619 T₃ = 567 SS₁ = 381.43 SS₂ = 185.71 SS₃ = 66 n₁ = 7 n₂ = 7 n₃ = 7 M₁ = 76.7143 M₂ = 88.4286 M₃ = 81.0000 You plan to use an ANOVA to test the impact of drinks with different caffeine contents on students’ test-taking abilities. What is the null hypothesis? The population mean test scores for all three treatments are equal. The population mean test scores for all three treatments are not all equal. The population mean test score for the water population is different from the population mean test score for the coffee population. The population mean test scores for all three treatments are different. Calculate the degrees of freedom and the variances for the following ANOVA table: Source SS df MS Between Within 633.14 Total 1,124.95 The formula for the F-ratio is: FF = = MSbetweenMSbetween / / MSwithinMSwithin Using words (chosen from the dropdown menu), the formula for the F-ratio can be written as: FF = = / / Using the data from the ANOVA table given, the F-ratio can be written as: FF = = / / Thus: FF = = Use the Distributions tool to find the critical region for α = 0.01. F Distribution Numerator Degrees of Freedom = 26 Denominator Degrees of Freedom = 26 012345678F At the α = 0.01 level of significance, what is your conclusion? You cannot reject the null hypothesis; caffeine does appear to affect test performance. You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance. You can reject the null hypothesis; caffeine does appear to affect test performance. You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.
Opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students’ test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later. The students receive the following arithmetic test scores: Water Coffee Espresso Caffeine Content (mg/oz) 0 13.4 51.3 78 92 83 ΣX² = 142,493 88 87 83 G = 1,723 72 80 76 N = 21 72 89 79 k = 3 64 96 86 81 83 79 82 92 81 T₁ = 537 T₂ = 619 T₃ = 567 SS₁ = 381.43 SS₂ = 185.71 SS₃ = 66 n₁ = 7 n₂ = 7 n₃ = 7 M₁ = 76.7143 M₂ = 88.4286 M₃ = 81.0000 You plan to use an ANOVA to test the impact of drinks with different caffeine contents on students’ test-taking abilities. What is the null hypothesis? The population mean test scores for all three treatments are equal. The population mean test scores for all three treatments are not all equal. The population mean test score for the water population is different from the population mean test score for the coffee population. The population mean test scores for all three treatments are different. Calculate the degrees of freedom and the variances for the following ANOVA table: Source SS df MS Between Within 633.14 Total 1,124.95 The formula for the F-ratio is: FF = = MSbetweenMSbetween / / MSwithinMSwithin Using words (chosen from the dropdown menu), the formula for the F-ratio can be written as: FF = = / / Using the data from the ANOVA table given, the F-ratio can be written as: FF = = / / Thus: FF = = Use the Distributions tool to find the critical region for α = 0.01. F Distribution Numerator Degrees of Freedom = 26 Denominator Degrees of Freedom = 26 012345678F At the α = 0.01 level of significance, what is your conclusion? You cannot reject the null hypothesis; caffeine does appear to affect test performance. You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance. You can reject the null hypothesis; caffeine does appear to affect test performance. You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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Question
7. Hypothesis testing with ANOVA
Opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students’ test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later.
The students receive the following arithmetic test scores:
|
|
Water
|
Coffee
|
Espresso
|
|
|---|---|---|---|---|
| Caffeine Content (mg/oz) | 0 | 13.4 | 51.3 | |
| 78 | 92 | 83 | ΣX² = 142,493 | |
| 88 | 87 | 83 | G = 1,723 | |
| 72 | 80 | 76 | N = 21 | |
| 72 | 89 | 79 | k = 3 | |
| 64 | 96 | 86 | ||
| 81 | 83 | 79 | ||
| 82 | 92 | 81 | ||
| T₁ = 537 | T₂ = 619 | T₃ = 567 | ||
| SS₁ = 381.43 | SS₂ = 185.71 | SS₃ = 66 | ||
| n₁ = 7 | n₂ = 7 | n₃ = 7 | ||
| M₁ = 76.7143 | M₂ = 88.4286 | M₃ = 81.0000 |
You plan to use an ANOVA to test the impact of drinks with different caffeine contents on students’ test-taking abilities. What is the null hypothesis?
The population mean test scores for all three treatments are equal.
The population mean test scores for all three treatments are not all equal.
The population mean test score for the water population is different from the population mean test score for the coffee population.
The population mean test scores for all three treatments are different.
Calculate the degrees of freedom and the variances for the following ANOVA table:
|
Source
|
SS
|
df
|
MS
|
|---|---|---|---|
| Between | |||
| Within | 633.14 | ||
| Total | 1,124.95 |
The formula for the F-ratio is:
| FF | = = | MSbetweenMSbetween | / / | MSwithinMSwithin |
Using words (chosen from the dropdown menu), the formula for the F-ratio can be written as:
| FF | = = | / / |
Using the data from the ANOVA table given, the F-ratio can be written as:
| FF | = = | / / |
Thus:
| FF | = = |
Use the Distributions tool to find the critical region for α = 0.01.
F Distribution
Numerator Degrees of Freedom = 26
Denominator Degrees of Freedom = 26
012345678F
At the α = 0.01 level of significance, what is your conclusion?
You cannot reject the null hypothesis; caffeine does appear to affect test performance.
You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.
You can reject the null hypothesis; caffeine does appear to affect test performance.
You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.
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