Manny Mevito wants to study whether the height (in inches) of an engineer determines how many complaints they get. He assumes the complaints are normally distributed, and that the variances should be pooled. The engineers are categorized according to whether they get few, some, or many complaints. The data is shown below, along with some calculations (which are done correctly). SomeManyFewData71.968.471.2 6874.564.4 66.469.872.2Averages68.870.969.3Std dev2.833.24.24Overall Average:69.67 (71.9−69.67)2+(68−69.67)2+(66.4−69.67)2+(68.4−69.67)2+(74.5−69.67)2+(69.8−69.67)2+(71.2−69.67)2+(64.4−69.67)2+(72.2−69.67)2 =79.6731000000001(10−1)6.52+(23−1)6.12+(12−1)7.32+(14−1)5.92=2237.59(3−1)(2.83)2+(3−1)(3.2)2+(3−1)(4.24)2 =72.453Use three decimal places in the table DFSSMSFGroups Error Total

A one-way ANOVA tests the significant difference in group means for more than two groups.

Answered: Manny Mevito wants to study whether the…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 3E

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Manny Mevito wants to study whether the height (in inches) of an engineer determines how many complaints they get. He assumes the complaints are normally distributed, and that the variances should be pooled. The engineers are categorized according to whether they get few, some, or many complaints. The data is shown below, along with some calculations (which are done correctly).

	Some	Many	Few
Data	71.9	68.4	71.2
	68	74.5	64.4
	66.4	69.8	72.2
Averages	68.8	70.9	69.3
Std dev	2.83	3.2	4.24
Overall Average:69.67

(71.9−69.67)²+(68−69.67)²+(66.4−69.67)²+

(68.4−69.67)²+(74.5−69.67)²+(69.8−69.67)²+

(71.2−69.67)²+(64.4−69.67)²+(72.2−69.67)²

=79.6731000000001

(10−1)6.5²+(23−1)6.1²+(12−1)7.3²+(14−1)5.9²=2237.59(3−1)(2.83)²+(3−1)(3.2)²+(3−1)(4.24)²

=72.453

Use three decimal places in the table

	DF	SS	MS	F
Groups
Error
Total

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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