Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter B.6, Problem 21AYU
Lower Your Cholesterol Researcher Francisco Fuentes and his colleagues wanted to determine the most effective diet for reducing LDL cholesterol, the so-called “bad” cholesterol, among three diets: (1) a saturated-fat diet: 15% protein, 47% carbohydrates, and 38% fat (20% saturated fat, 12% monounsaturated fat, and 6% polyunsaturated fat); (2) the Mediterranean diet: 47% carbohydrates, and 38% fat (10% saturated fat, 22% monounsaturated fat, and 6% polyunsaturated fat); and (3) the US National Cholesterol Education Program or NCEP-1 Diet: 10% saturated fat, 12% monounsaturated fat, and 6% polyunsaturated fat. Participants in the study were shown to have the same levels of LDL cholesterol before the study and were randomly assigned to one of the three diets, or treatment groups. After 28 days, their LDL cholesterol levels were recorded. The data in the following table are based on this study.
- (a) Why is this study a completely randomized design?
- (b) What is the response variable? What is the explanatory variable that is controlled and set at three levels?
- (c) The participants were randomly assigned to one of three treatment groups. What is the purpose of randomization in this study?
- (d) State the null and alternative hypotheses.
- (e) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from normal populations.
- (f) Are the
mean LDL cholesterol levels different at the α = 0.05 level of significance? - (g) Draw boxplots of the LDL cholesterol levels for the three groups to support the analytic results obtained in part (f).
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You get a job as the manager of a popular ice cream store in your hometown. One of your first concerns is determining how much ice cream you should stock to meet the demands of your customers. You suspect that the number of customers buying ice cream probably depends on several factors.
In looking through company files, you discover that the former manager collected considerable data. Last summer, a typical week produced the following data:
Day
Temperature (degrees Fahrenheit)
Number of Transactions
Gross Receipts (in dollars)
Monday
78
238
3014
Tuesday
73
194
2842
Wednesday
70
172
2141
Thursday
75
185
2235
Friday
83
270
4505
Saturday
89
320
5021
Sunday
94
280
4442
On the graph below, the temperature is graphed on the x axis and the number of transactions is graphed on the y axis.
Investigate the relationship between the temperature and the gross receipts. On the grid below, graph…
Some commercial airlines recirculate about half the air in the cabin during flights as a way to improve fuel efficiency. Other airlines make a policy of NOT recirculating the air and instead, have fresh air from the atmosphere constantly being inserted into the cabin with the “old” air being pumped out of the plane.
A total of 1100 passengers flying from San Francisco to Denver were used for an experiment. After their flight, they were each given a list of symptoms associated with the common cold. They were asked to report if they experienced cold symptoms within 24 hours of the flight landing.
Of the 517 passengers who flew on planes that recirculate the air, 108 reported post-flight cold symptoms. Of the 583 passengers who flew on airlines that do not use recirculation in the cabin, 110 reported symptoms.
Suppose now that we want to use the recirculation of air data to explore “Goal #2”, which is to resolve a hypothesis test about .
a) If we want to resolve this hypothesis…
Chapter B.6 Solutions
Fundamentals of Statistics (5th Edition)
Ch. B.6 - The acronym ANOVA stands for __________ __...Ch. B.6 - True or False: To perform a one-way ANOVA, the...Ch. B.6 - True or False: To perform a one-way ANOVA, the...Ch. B.6 - The variability among the sample means is called...Ch. B.6 - The variability within each treatment group, which...Ch. B.6 - True or False: The F-test statistic is F0=MSTMSE.Ch. B.6 - In Problems 7 and 8, fill in the ANOVA table. 7.Ch. B.6 - In Problems 7 and 8, fill in the ANOVA table. 8.Ch. B.6 - In Problems 9 and 10, determine the F-test...Ch. B.6 - In Problems 9 and 10, determine the F-test...
Ch. B.6 - NW 11. The following data represent a simple...Ch. B.6 - The following data represent a simple random...Ch. B.6 - NW 13. Corn Production The data in the table...Ch. B.6 - Soybean Yield The data in the table represent the...Ch. B.6 - Which Delivery Method Is Best? At a community...Ch. B.6 - Births by Day of Week An obstetrician knew that...Ch. B.6 - Rates of Return A stock analyst wondered whether...Ch. B.6 - Reaction Time In an online psychology experiment...Ch. B.6 - Car-Buying Discrimination To determine if there is...Ch. B.6 - Crash Data The Insurance Institute for Highway...Ch. B.6 - Lower Your Cholesterol Researcher Francisco...Ch. B.6 - pH in Rain An environmentalist wanted to determine...Ch. B.6 - Age and Politics Do peoples political philosophy...Ch. B.6 - Concrete Strength An engineer wants to know if the...Ch. B.6 - Analyzing Journal Article Results Researchers...Ch. B.6 - Prob. 27AYUCh. B.6 - Diversity and pH The following data represent the...Ch. B.6 - Another E-Cig Study In a study of adult smokers...Ch. B.6 - What are the requirements to perform a one-way...Ch. B.6 - What is the mean square due to treatment estimate...Ch. B.6 - Why does a large value of the F statistic provide...Ch. B.6 - In a one-way ANOVA, explain what it means to...
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