Problem Set: Chapter 12 Introduction to Analysis of Variance The following table summarizes the results of a study on SAT prep courses, comparing SAT Scores of students in a private preparation class, a high school preparation class, and no preparation class. Use the information from the table to answer the remaining questions. Number of Observations Sample Mean Sum of Squares (SS) Treatment Private prep class 60 650 132,750.00 High school prep class 60 645 147,500.00 No prep class 60 625 162,250.00 Using the data provided, complete the partial ANOVA summary table that follows. (Hint: T, the treatment total, can be calculated as the sample mean times the number of observations. G, the grand total, can be calculated from the values of T once you have calculated them.) Sum of Squares (SS) Mean Square (MS) Source df Between treatments Within treatments In some ANOVA summary tables you will see, the labels in the first (source) column are Treatment, Error, and Total. Which of the following reasons best explains why the within-treatments variance is sometimes referred to as the "error variance"? O The within-treatments variance measures random, unsystematic differences within each of the samples assigned to each of the treatments. These differences are not due to treatment effects because everyone within each sample received the same treatment; therefore, the differences are sometimes referred to as "error." The within-treatments variance measures treatment effects as well as random, unsystematic differences within each of the samples assigned to each of the treatments. These differences represent all of the variations that could occur in a study; therefore, they are sometimes referred to as "error." Differences among members of the sample who received the same treatment occur when the researcher makes an error, and thus these
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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Problem Set: Chapter 12 Introduction to Analysis of Variance
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O Catalog and Study Tools
Source
Sum of Squares (SS)
df
Mean Square (MS)
Between treatments
А-Z
Partner Offers
Within treatments
Rental Options
In some ANOVA summary tables you will see, the labels in the first (source) column are Treatment, Error, and Total. Which of the following reasons
best explains why the within-treatments variance is sometimes referred to as the "error variance"?
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The within-treatments variance measures random, unsystematic differences within each of the samples assigned to each of the
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treatments. These differences are not due to treatment effects because everyone within each sample received the same treatment;
therefore, the differences are sometimes referred to as "error."
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The within-treatments variance measures treatment effects as well as random, unsystematic differences within each of the samples
assigned to each of the treatments. These differences represent all of the variations that could occur in a study; therefore, they are
NO
sometimes referred to as "error."
Differences among members of the sample who received the same treatment occur when the researcher makes an error, and thus these
differences are sometimes referred to as "error."
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Differences among members of the sample who received the same treatment occur because some treatments are more effective than
others, so it would be an error to receive the less superior treatments.
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In ANOVA, the F test statistic is the
of the between-treatments variance and the within-treatments variance. The value of the F test
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statistic is
When the null hypothesis is true, the F test statistic is
When the null hypothesis is false, the F test statistic is most likely
In general, you should reject the null hypothesis for
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Problem Set: Chapter 12 Introduction to Analysis of Variance
The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high
Courses
school preparation class, and no preparation class. Use the information from the table to answer the remaining questions.
Catalog and Study Tools
А-Z
Treatment
Number of Observations
Sample Mean
Sum of Squares (SS)
Partner Offers
Private prep class
60
650
132,750.00
Rental Options
High school prep class
60
645
147,500.00
No prep class
60
625
162,250.00
College Success Tips
Career Success Tips
Using the data provided, complete the partial ANOVA summary table that follows. (Hint: T, the treatment total, can be calculated as the sample mean
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times the number of observations. G, the grand total, can be calculated from the values of T once you have calculated them.)
Source
Sum of Squares (SS)
df
Mean Square (MS)
Between treatments
Within treatments
Managing Your Study Time
In some ANOVA summary tables you will see, the labels in the first (source) column are Treatment, Error, and Total. Which of the following reasons
best explains why the within-treatments variance is sometimes referred to as the "error variance"?
Help
The within-treatments variance measures random, unsystematic differences within each of the samples assigned to each of the
Give Feedback
treatments. These differences are not due to treatment effects because everyone within each sample received the same treatment;
therefore, the differences are sometimes referred to as "error."
The within-treatments variance measures treatment effects as well as random, unsystematic differences within each of the samples
assigned to each of the treatments. These differences represent all of the variations that could occur in a study; therefore, they are
sometimes referred to as "error."
Differences among members of the sample who received the same treatment occur when the researcher makes an error, and thus these
differences are sometimes referred to as "error."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F074fc4e5-d622-4836-9d1a-a419572349db%2F7880dca4-5e76-4632-9110-633f08823a5f%2Fx2q4dpr_processed.png&w=3840&q=75)
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