Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Textbook Question
Chapter 11, Problem 89CR
Here’s one to sink your teeth into: The authors of the article “Analysis of Food Crushing Sounds During Mastication: Total Sound Level Studies” (Journal of Texture Studies [1990]: 165–178) studied the nature of sounds generated during eating. Peak loudness (in decibels at 20 cm away) was measured for both open-mouth and closed-mouth chewing of potato chips and of tortilla chips. Forty subjects participated, with ten assigned at random to each combination of conditions (such as closed-mouth potato chip, and so on). We are not making this up! Summary values taken from plots given in the article appear in the accompanying table. For purposes of this exercise, suppose that it is reasonable to regard the peak loudness distributions as approximately normal.
- a. Construct a 95% confidence interval tor the (inference in mean peak loudness between open-mouth and closed-mouth chewing of potato chips. Interpret the resulting interval.
- b. For closed-mouth chewing (the recommended method!), is there sufficient evidence to indicate that there is a difference between potato chips and tortilla chips with respect to mean peak loudness? Test the relevant hypotheses using α = 0.01.
- c. The means and standard deviations given here were actually for stale chips. When ten measurements of peak loudness were recorded for closed-mouth chewing of fresh tortilla chips, the resulting mean and standard deviation were 56 and 14, respectively. Is there sufficient evidence to conclude that chewing fresh tortilla chips is louder than chewing stale chips? Use α = 0.05.
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An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.
Beverage
Sample Size
Sample Mean
Sample SD
Strawberry Drink
10
535
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Cola
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559
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? = 0.05.)
State the relevant hypotheses. (Use ?1 for the strawberry drink and ?2 for the cola.)
H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≥ 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0 H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0
Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)
t
=
P-value
=
State the conclusion in the problem context.
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The following data are from a random sample of 10 students who participated in a study undertaken to investigate the effect of sleep time (measured in average number of hours of sleep per night) on GPA (grade point average, measured on a 4-point scale).
Student
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1
7
3.28
2
9
3.16
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3.75
4
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5
4
2.45
6
8
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6
3.02
9
3
2.30
10
8
3.48
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b. What is the estimated GPA of a student who averages 5 hours of sleep per night?
c. What is the coefficient of determination?
*(no use EXCEL)
Chapter 11 Solutions
Introduction To Statistics And Data Analysis
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