MATH 1P98 Lecture Notes - Lecture 13: Null Hypothesis, F-Test, F-Distribution

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cyanscorpion172

2 Feb 2016

School

Brock University

Department

Mathematics and Statistics

Course

MATH 1P98

Professor

Susanna Spektor

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$MATH 1P98 Full Course Notes$

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The ratio of two independent chi-square variables divided by their respective degrees of freedom. If the population variances are equal, this simplifies to be the ratio of the sample variances. A technique used to test a hypothesis concerning the means of three or mor populations. Analysis of variance when there is only one independent variable. The variation due to the interaction between the samples, denoted ss(b) for sum of. If the sample means are close to each other (and therefore the. The variance due to the interaction between the samples, denoted ms(b) for mean. The variation due to differences within individual samples, denoted ss(w) for sum of. The variance due to the differences within individual samples, denoted ms(w) for mean. A test used to find where the differences between means lie when the analysis of. The scheffe" test is generally used when the sample sizes are different.

Related Questions

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:

	Cola	Black Tea	Coffee
Caffeine Content (mg/oz)	2.9	5.9	13.4
	85	85	92	∑X² = 147,641
	86	89	87	G = 1,755
	82	82	80	N = 21
	75	75	89	k = 3
	66	88	96
	78	76	83
	87	82	92
	T₁ = 559	T₂ = 559	T₃ = 559
	SS₁ = 338.86	SS₂ = 338.86	SS₃ = 338.86
	n₁ = 7	n₂ = 7	n₃ = 7
	M₁ = 79.8571	M₂ = 79.8571	M₃ = 79.8571

1.) 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?

(a) The population mean test score for the cola population is different from the population mean test score for the black tea population.

(b) The population mean test scores for all three treatments are equal.

(d) The population mean test scores for all three treatments are not all equal.

2.) Calculate the degrees of freedom and the variances for the following ANOVA table:

Source	SS	df	MS
Between	-	-	-
Within	702.28	-	-
Total	973.14	-

The formula for the F-ratio is:

3.) Using words, the formula of the F-ratio can be written as:

4.) Using the data from the ANOVA table given, the F-ratio can be written as:

5.) Calculate for F-ratio:

6.) At the level of significance, what is your conclusion?

(a)You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.

(b)You cannot reject the null hypothesis; caffeine does appear to affect test performance.

(c)You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.

(d)You can reject the null hypothesis; caffeine does appear to affect test performance.

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MATH 1P98 Lecture Notes - Lecture 13: Null Hypothesis, F-Test, F-Distribution

MATH 1P98 Full Course Notes

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