Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 12.3, Problem 26AYU
Why is it desirable to have the explanatory variables spread out to test a hypothesis regarding β1 or to construct confidence intervals about β1?
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A study was conducted that measured the total brain volume (TBV) (in mm³) of patients that had
schizophrenia and patients that are considered normal. The first table contains the TBV of the non-
schizophrenic patients and the second table contains the TBV of schizophrenia patients. Compute a 95%
confidence interval for the difference in TBV of non-schizophrenic patients and patients with
Schizophrenia. Prior studies say nothing about the equality of variances. Round to the nearest whole
number.
Total Brain Volume (in mm³) of Non-Schizophrenic Patients
1493670 1505354 1642063 1269967 1520437 1581952 1550295
1549683 1338983 1422347 1492283 1195153 1396509 1478392
1485412 1618109 1459455 1717233 1357073 1576932 1417992
1548420 1484842 1595374 1679448 1569374 1370347 1389635
1396599 1533894 1565016 1340012
Total Brain Volume (in mm³) of Schizophrenia Patients
1274453 1212643 1523072 1543675 1466250 1299458 1283251
1592091 1730346 1074105 1362385 1435833 1603966 1523104
1248181 1424469…
A study was conducted that measured the total brain volume (TBV) (in mm³) of patients that had
schizophrenia and patients that are considered normal. The first table contains the TBV of the non-
schizophrenic patients and the second table contains the TBV of schizophrenia patients. Compute a 99%
confidence interval for the difference in TBV of non-schizophrenic patients and patients with
Schizophrenia. Prior studies say nothing about the equality of variances. Round to the nearest whole
number.
Total Brain Volume (in mm³) of Non-Schizophrenic Patients
1409670 1528399 1541583 1652404 1668272 1606774 1549862
1497601 1525728 1487617 1556951 1484397 1371703 1472556
1455624 1430001 1297891 1365193 1362972 1542673 1483211
1353428 1371403 1663617 1415307 1756698 1340146 1528697
1673225 1456134 1427036 1144683
Total Brain Volume (in mm³) of Schizophrenia Patients
1348795 1093447 1575546 1183986 1363837 1381758 1265598
1137626 1342077 1339149 1317181 1570744 1409139 1242976
1511787 1171081…
Is there sufficient evidence to indicate the overall model is statistically useful for predicting y. Test using α=10%. Make sure you include, in your answer, the null and alternative hypotheses, the value of an appropriate test statistic, the p-value AND rejection region, and conclusion.
Find the 95% confidence interval for β3. Use the interval to determine if mood scores would be useful to the model if both intrapersonal and stress management scores are already included in the model and give a brief explanation.
TestH0: β2=0 against H0: β2>0 at α=05. Make sure you include, in your answer, the value of an appropriate test statistic, p-value AND rejection region, and conclusion.
Chapter 12 Solutions
Fundamentals of Statistics (5th Edition)
Ch. 12.1 - True or False: The shape of the chi-square...Ch. 12.1 - A _____ test is an inferential procedure used to...Ch. 12.1 - Suppose there are n independent trials of an...Ch. 12.1 - What are the two requirements that must be...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - Prob. 7AYUCh. 12.1 - Prob. 8AYUCh. 12.1 - In Problems 710, determine (a) the 2 test...Ch. 12.1 - In Problems 710, determine (a) the 2 test...
Ch. 12.1 - Applying the Concepts 11. NW Plain MMs According...Ch. 12.1 - Peanut MMs According to the manufacturer of MMs,...Ch. 12.1 - Prob. 13AYUCh. 12.1 - Prob. 14AYUCh. 12.1 - Always Wear a Helmet The National Highway Traffic...Ch. 12.1 - Religion in Congress Is the religious make-up of...Ch. 12.1 - Does It Matter Where I Sit? Does the location of...Ch. 12.1 - Racial Profiling On January 1, 2004, it became...Ch. 12.1 - Prob. 19AYUCh. 12.1 - Prob. 20AYUCh. 12.1 - Prob. 21AYUCh. 12.1 - Is the Die Loaded? A player in a craps game...Ch. 12.1 - Grade Distributions At Joliet Junior College, the...Ch. 12.1 - Population Shift An urban economist wonders if the...Ch. 12.1 - Prob. 25AYUCh. 12.1 - Living Alone? In 2000, 25.8% of Americans 15 years...Ch. 12.1 - Putting It Together: The V-2 Rocket in London In...Ch. 12.1 - Putting It Together: Weldons Dice On February 2,...Ch. 12.1 - Buying a New Car How much does the typical person...Ch. 12.1 - Why is goodness of fit a good choice for the title...Ch. 12.1 - Explain why chi-square goodness-of-fit tests are...Ch. 12.1 - Prob. 32AYUCh. 12.2 - True or False: The expected frequencies in a...Ch. 12.2 - In a chi-square test for ____ of proportions, we...Ch. 12.2 - The following table contains observed values and...Ch. 12.2 - The table in the next column contains observed...Ch. 12.2 - Prob. 5AYUCh. 12.2 - Prob. 6AYUCh. 12.2 - NW Family Structure and Sexual Activity A...Ch. 12.2 - Prenatal Care An obstetrician wants to learn...Ch. 12.2 - Health and Happiness Are health and happiness...Ch. 12.2 - Health and Education Does amount of education play...Ch. 12.2 - Social Well-Being and Obesity The Gallup...Ch. 12.2 - Profile of Smokers The following data represent...Ch. 12.2 - Efficacy of e-Cigs Do electronic cigarettes assist...Ch. 12.2 - Celebrex Celebrex, a drug manufactured by Pfizer,...Ch. 12.2 - NW Whats in a Word? In a recent survey conducted...Ch. 12.2 - Whats in a Word? Part II In a recent survey...Ch. 12.2 - Dropping a Course A survey was conducted at a...Ch. 12.2 - Prob. 18AYUCh. 12.2 - Prob. 19AYUCh. 12.2 - Prob. 20AYUCh. 12.2 - Putting It Together: Women, Aspirin, and Heart...Ch. 12.2 - Homeruns Go to...Ch. 12.2 - Explain the differences between the chi-square...Ch. 12.2 - Why does the test for homogeneity follow the same...Ch. 12.3 - Suppose a least-squares regression line is given...Ch. 12.3 - Prob. 2AYUCh. 12.3 - Prob. 3AYUCh. 12.3 - Prob. 4AYUCh. 12.3 - Prob. 5AYUCh. 12.3 - Prob. 6AYUCh. 12.3 - Prob. 7AYUCh. 12.3 - Prob. 8AYUCh. 12.3 - Prob. 9AYUCh. 12.3 - Prob. 10AYUCh. 12.3 - An Unhealthy Commute The following data represent...Ch. 12.3 - Credit Scores An economist wants to determine the...Ch. 12.3 - Height versus Head Circumference A pediatrician...Ch. 12.3 - Hurricanes The data in the next column represent...Ch. 12.3 - Concrete As concrete cures, it gains strength. The...Ch. 12.3 - Tar and Nicotine Every year the Federal Trade...Ch. 12.3 - Invest in Education Go to...Ch. 12.3 - American Black Bears In 1969, Dr. Michael R....Ch. 12.3 - CEO Performance (Refer to Problem 31 in Section...Ch. 12.3 - Bear Markets (Refer to Problem 32. Section 4.1) A...Ch. 12.3 - Age versus HDL Cholesterol A doctor wanted to...Ch. 12.3 - Prob. 22AYUCh. 12.3 - Influential Observations Zillow.com is a site that...Ch. 12.3 - Why is it important to perform graphical as well...Ch. 12.3 - Prob. 25AYUCh. 12.3 - Why is it desirable to have the explanatory...Ch. 12.4 - Intervals constructed about the predicted value of...Ch. 12.4 - Prob. 2AYUCh. 12.4 - Prob. 3AYUCh. 12.4 - Using the sample data from Problem 6 in Section...Ch. 12.4 - Prob. 5AYUCh. 12.4 - Prob. 6AYUCh. 12.4 - Prob. 7AYUCh. 12.4 - Prob. 8AYUCh. 12.4 - Prob. 9AYUCh. 12.4 - Prob. 10AYUCh. 12.4 - Prob. 11AYUCh. 12.4 - Tar and Nicotine Use the results of Problem 16 in...Ch. 12.4 - Prob. 13AYUCh. 12.4 - Prob. 14AYUCh. 12.4 - CEO Performance Use the results of Problem 19 from...Ch. 12.4 - Prob. 16AYUCh. 12.4 - Prob. 17AYUCh. 12 - Roulette Wheel A pit boss suspects that a roulette...Ch. 12 - Prob. 2RECh. 12 - Titanic With 20% of men, 74% of women, and 52% of...Ch. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Seat Choice and GPA A biology professor wants to...Ch. 12 - Apartments The following data represent the square...Ch. 12 - Calories versus Sugar The following data represent...Ch. 12 - A pit boss is concerned that a pair of dice being...Ch. 12 - Prob. 2CTCh. 12 - The Harris Poll asked a random sample of adult...Ch. 12 - Prob. 4CTCh. 12 - Prob. 5CTCh. 12 - Prob. 6CTCh. 12 - Crickets make a chirping noise by sliding their...Ch. 12 - The following data represent the height (inches)...Ch. 12 - A researcher believes that as age increases, the...Ch. 12 - CASE STUDY Feeling Lucky? Well, Are You? In fiscal...
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