Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Textbook Question
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?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A recent poll of 1900 randomly selected 18-25-year-olds
revealed that 220 currently use marijuana or hashish.
According to a publication, 12.6 % of 18-25-year-olds were
current users of marijuana or hashish in 1997. Do the data
provide sufficient evidence to conclude that the percentage of
18-25-year-olds who currently use marijuana or hashish has
changed from the 1997 percentage of 12.6% ? Use α = 0.01
significance level.
test statistic z =
positive critical score
negative critical z score
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…
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...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Allopurinol test is often used as a screening device of potential carriers whose relatives are OTCD (a disorder of the urea cycle) patients. The sensitivity and the specificity of the allopurinol test are estimated as 0.927 and 0.997, respectively. If the prevalence of individuals with OTCD in the population is 1/32000, determine the predictive value negative of the allopurinol screening test.arrow_forwardReports show that 92% of online searches in March 2021 use Google as the search engine.A network administrator wants to determine whether the percentage of searches that useGoogle is different in their company. They sample 800 searches and find that 758 of themuse Google. Can they conclude that the percentage of searches that use Google in thiscompany differs from 92%? Use the α = 0.05 level of significance.arrow_forwardProductivity is the key driver of wages and one of the most importantdeterminants of living standards. The British Chambers of Commercecommissioned research into understanding whether labour productivity in theautomotive manufacturing sector in England and Ireland were the same ordifferent. The researchers collected data on a random sample of 8 firms inEngland and 4 in Ireland and recorded productivity in units of value added (£)per hour. It is assumed that firm-level productivity has a normal distribution.The following data were collected:Ireland 47 56 43 68England 39 50 39 45 50 43 35 43(i) Set up appropriate null and alternative hypotheses and conduct a test ofthe hypotheses of equal mean productivity in Ireland and England at 5 percent significance level under the assumption of unknown but equalpopulation variances. Provide as much detail as possible on yourprocedures. Clearly show all your steps in testing and state your decision.Discuss the economic implications of your findings.…arrow_forward
- What source of variation is found in an ANOVA summary table for a within subjects design that is not in an ANOVA summary table for a between subjects design. What happens to this source of variation in a between-subjects design?arrow_forwardA research study conducts a one-tailed test with an alpha level or significance value of 10% and a sample size of 12. What critical value or t-test value (from the table) should be compared to the t value obtained as the test statistic? What is the t- value if the coefficient of correlation is 3.5? Is there a correlation between the variables and not accept the null hypothesis?arrow_forwardA) Perform a formal test for correlation on the chocolate consumption / Nobel prize winners data in chocolate nobels H0: There is no correlation between chocolate consumption and the number of Nobel prize winners (=0) H1: There is a correlation between chocolate consumption and the number of Nobel prize winners ( is not 0) What is the critical value of Spearman's correlation coefficient, which is required to reject the null hypothesis at a 0.05 confidence level? B) Perform a formal test for correlation on the chocolate consumption / Nobel prize winners data in chocolate nobels H0: There is no correlation between chocolate consumption and the number of Nobel prize winners (=0) H1: There is a correlation between chocolate consumption and the number of Nobel prize winners ( is not 0) True or false: The null hypothesis should be rejected based on your analysis in the preceding questions.arrow_forward
- Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 90th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 1 . Table 1 Pilot data on left ventricular mass (LVM) in children from the Bogalusa Heart Study ID Baseline LVM (g) 4- year LVM (g) Change (g)* 1 139 163 24 2 134 126 -8 3 86 142 56…arrow_forwardLeft ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 90th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 1 . Table 1 Pilot data on left ventricular mass (LVM) in children from the Bogalusa Heart Study ID Baseline LVM (g) 4- year LVM (g) Change (g)* 1 139 163 24 2 134 126 -8 3 86 142 56…arrow_forwardFind the value of the test statistic and find the 5% critical valuearrow_forward
- A psychologist would like to examine the effects of different testing methods on the final performance of college students. One group has regular quizzes, one group has three large exams, and the third group only has a final exam. At the end of the course, the psychologist interviews each student to get a measure of the student’s overall knowledge of the material. Do these data indicate any significant differences among the three methods? Test with α = .05. Include a source table for this ANOVA and state whether your F ratio is significant. Calculate the η2 value for this effect and Compute Tukey’s HSD to determine exactly which methods are significantly different.arrow_forwardYou are comparing freshmen and seniors at your college on hours spent studying per day. You pick a sample of 11 people from each group. For freshmen, the mean was 3 and the variance was 1.2. For seniors, the mean was 2 and the variance was 1. Calculate a 90% confidence interval on the difference between means (freshmen - seniors). What is the lower limit of this CI?arrow_forwardLeft ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 9.18 (Note: These are the same data as in Table 8.27, p. 329). 9.71 Compare your results in Problems 9.69 and 9.70. 9.72 Compare your results to those obtained using t test methods in Problem…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Type I and II Errors, Power, Effect Size, Significance and Power Analysis in Quantitative Research; Author: NurseKillam;https://www.youtube.com/watch?v=OWn3Ko1WYTA;License: Standard YouTube License, CC-BY