A researcher hypothesizes that different colors of cars result in different average speeds. To test this claim, she took a random sample of 20 people who own 4 different colors of colors of cars (n = 20, N = 80, G = 4), and she then tracks their average speed on the highway for a week of driving. The following ANOVA table has some of her results. Please help her answer her research questions by completing the following ANOVA table below and answering the follow-up questions. Be sure to label your answers with the appropriate letter and show all your work!
A researcher hypothesizes that different colors of cars result in different average speeds. To test this claim, she took a random sample of 20 people who own 4 different colors of colors of cars (n = 20, N = 80, G = 4), and she then tracks their average speed on the highway for a week of driving. The following ANOVA table has some of her results. Please help her answer her research questions by completing the following ANOVA table below and answering the follow-up questions. Be sure to label your answers with the appropriate letter and show all your work!
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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- A researcher hypothesizes that different colors of cars result in different average speeds. To test this claim, she took a random sample of 20 people who own 4 different colors of colors of cars (n = 20, N = 80, G = 4), and she then tracks their average speed on the highway for a week of driving. The following ANOVA table has some of her results.
- Please help her answer her research questions by completing the following ANOVA table below and answering the follow-up questions. Be sure to label your answers with the appropriate letter and show all your work!
| Source | Sums of Squares | df | Mean Square | F |
| Effect (between) | ||||
| Error (within) | 100.90 | ------ | ||
| Total | 170.10 | ------- | ------ |
a) What is the Sums of Squares (SS) between (effect)?
b) What are the Mean Square (MS) between (effect) and the MS within (error)?
c) What are the degrees of freedom (df) between, the df within, and the df total?
d) What is the overall F-statistic?
e) Based on the observed F-statistic (α = 0.05) and a critical F = 2.47, should she retain or reject the null hypothesis?
f) In everyday language, what can she conclude about the research question?
Suppose that the average speed for Red Cars was 72.5 and the average speed for White Cars was 68.2.
a) Calculate and report (including the degrees of freedom) a follow-up t-test using an α (alpha) = 0.05 and a critical t = 1.98.
b) In everyday language, what can she conclude about how people who drive red versus white cars?
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