Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 8.1, Problem 7E
Vitamin B6 is one of the vitamins in a multiple vitamin pill manufactured by a pharmaceutical company. The pills are produced with a
A consumer group suspects that
(a) Define a critical region to test
(b) If the 20 pills yielded a mean of
(c) What is the approximate p-value of this test?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, and adult male patient has taken 13 blood test for uric acid. The main concentration was X=5.41 mg/dl. The distribution of uric acid and healthy adult meals can be assumed to be normal, with o=1.81 mg/dl. find a 95% confidence interval for the population mean concentration of uric acid in the patient's blood. What is the margin of error? (Round your answers to two decimal places.)
lower limit=
upper limit=
Does the potency of drug reduce after one year in storage?
To test this, researchers plan to compare the average potency of a sample of recently produced bottles of the drug with the average potency of a sample of bottles of the drug that have been stored for a year.
They will test for evidence that the mean potency score for the fresh drug (µ1) is higher than the mean potency score for the stored drug (µ2).
Based on the information provided, which of the following sets of hypotheses is appropriate for the test?
Hint: We first cover inference for a difference in means in Section 6.4.
Select one:
a.H0: μ1 - μ2 ≤ 0, Ha: μ1 - μ2 = 0
b.H0: μ1 - μ2 = 0, Ha: μ1 - μ2 > 0
c.H0: μ1 - μ2 = 0, Ha: μ1 - μ2 < 0
d.H0: μ1 - μ2 = 0, Ha: μ1 - μ2 ≠ 0
Retinitis pigmentosa (RP) is a hereditary ocular diseasein which patches of pigment appear on the retina, potentially resulting in substantial vision loss and in somecases complete blindness. An important issue is how fastthe subjects decline. Visual field is an important measureof area of vision, which is measured in degree2. A visualfield area for a normal person is around 11,000 degree2.The longitudinal data in Table 11.29 were provided by anindividual patient.Table 11.29 Longitudinal visual field data forone RP patientTime Visual field area lnVisit (yr) (degree2) (visual field area)1 0 3059 8.032 1 3053 8.023 2 1418 7.264 3 1692 7.435 4 1978 7.596 5 1567 7.367 6 1919 7.568 7 1998 7.609 11 1648 7.4110 13 1721 7.4511 15 1264 7.14mean 6.09 1938 7.532sd 4.97 597 0.280Suppose the rate of change of ln (visual field) is a linearfunction of follow-up time.11.103 Write down a linear regression model that summarizes this relationship.
Chapter 8 Solutions
Probability and Statistical Inference (9th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Similar questions
- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardRetinitis pigmentosa (RP) is a hereditary ocular diseasein which patches of pigment appear on the retina, potentially resulting in substantial vision loss and in somecases complete blindness. An important issue is how fastthe subjects decline. Visual field is an important measureof area of vision, which is measured in degree2. A visualfield area for a normal person is around 11,000 degree2.The longitudinal data in Table 11.29 were provided by anindividual patient.Table 11.29 Longitudinal visual field data forone RP patientTime Visual field area lnVisit (yr) (degree2) (visual field area)1 0 3059 8.032 1 3053 8.023 2 1418 7.264 3 1692 7.435 4 1978 7.596 5 1567 7.367 6 1919 7.568 7 1998 7.609 11 1648 7.4110 13 1721 7.4511 15 1264 7.14mean 6.09 1938 7.532sd 4.97 597 0.280Suppose the rate of change of ln (visual field) is a linearfunction of follow-up time.11.103 Write down a linear regression model that summarizes this relationship.11.104 Fit the regression line using the method of…arrow_forwardDo wearable devices that monitor diet and physical activity help people lose weight? Researchers had 237 subjects who were already involved in a program of diet and exercise use wearable technology for 24 months. They measured their weight (in kilograms) before using the technology and 24 months after using the technology. The 237 differences in weight (weight after 24 months minus weight before using the wearable technology) had x = -3.5 and s = 7.8. Let u be the mean weight difference. 41 John M. Jakicic et al., "Effect of wearable technology combined with a lifestyle intervention on long-term weight loss, the IDEA randomized clinical trial," JAMA, 316, 2016, pp. 1161-1171. O Macmillan Learning " What is the test statistic? Give your answer to three decimal places. What is the P-value? The P-value is between 0.01 and 0.05. The P-value is less than 0.0005. O The P-value is between 0.0005 and 0.01. The P-value is greater than 0.05.arrow_forward
- A methodological study had established values for the MIC on a scale that measured physical function: The MIC for improvement (higher scores) was 4.0, and the MIC for deterioration (lower scores) was 3.0. Lawrence studied clinically significant change in physical functioning over a 1-year period for a sample of 100 patients with COPD. Some change score information is presented below for 10 patients. Which patients experienced clinically significant change in physical function in the 12-month period between assessments? Patient Baseline Score* 12-Month Score* 1 19 15 2 12 10 3 16 14 4 17 16 5 9 10 6 11 12 7 13 17 8 15 13 9 18 14 10 16 9 *Higher scores = higher level of physical function Which patients had clinically significant deterioration? Which patients had clinically significant improvement? Which patients had no clinically significant change?arrow_forwardAlbumin is a liver protein that helps circulate vitamins throughout the body. Reduced Albumin has been associated with severe illness with Covid-19 patients. Suppose we wanted to conduct a study to compare the mean Albumin concentration (g/L) between a sample of adult patients hospitalized for Covid 19 (Sample Mean= 32.8, s=6.0) to the mean albumin concentration (g/L) of healthy adults (u=34.1, o=7.13). How many patients would need to enroll from the hospital to conduct this study with 99% confidence, and 80% power? A. 267 B. 120 C. 352 D. 225arrow_forwardTo check the effect of hot temperatures on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a warm car in the sun for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before the breakage is measured on each rubber band, and the mean for the hot bands is compared to the mean for the others. Is this a good experimental design? No, because No, because temperature is confounded No, because No, because the means are more than two more not proper Yes brands should temperatures should be used. statistics for be used. with brand. comparison.arrow_forward
- OphthalmologyRetinitis pigmentosa (RP) is a hereditary ocular diseasein which patches of pigment appear on the retina, potentially resulting in substantial vision loss and in somecases complete blindness. An important issue is how fastthe subjects decline. Visual field is an important measureof area of vision, which is measured in degree2. A visualfield area for a normal person is around 11,000 degree2.The longitudinal data in Table 11.29 were provided by anindividual patient.Table 11.29 Longitudinal visual field data forone RP patientTime Visual field area lnVisit (yr) (degree2) (visual field area)1 0 3059 8.032 1 3053 8.023 2 1418 7.264 3 1692 7.435 4 1978 7.596 5 1567 7.367 6 1919 7.568 7 1998 7.609 11 1648 7.4110 13 1721 7.4511 15 1264 7.14mean 6.09 1938 7.532sd 4.97 597 0.280Suppose the rate of change of ln (visual field) is a linearfunction of follow-up time.11.103 Write down a linear regression model that summarizes this relationship.11.104 Fit the regression line using…arrow_forwardA researcher is interested in testing the relationship between smoking and BMI (kg/m2) in adults aged 30-45. In order to test this association, the researcher divides smoking into currently more than a pack a day, currently less than a pack a day, and never smokers. The following table represents the BMIs for each participant enrolled by their respective smoking category. Current Smoker (≥1pack/day) Current Smoker (<1 pack/day Never Smoked 26.7 29.4 22.1 29.4 28.6 30.4 24.3 27.4 21.3 28.4 23.2 26.4 21.6 20.1 19.7 27.4 20.6 19.8 26.8 19.7 21.6 36.4 19.6 22.3 31.5 21.6 24.3 27.4 21.5 *Continue as though all assumptions for ANOVA are met. A) Calculate the MSW and MSB for the data represented above. B) Carry out a formal test for a one-way analysis of variance among the groups and interpret your results.arrow_forwardStudies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered? The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitation center (in which cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes: Mean call-to-shock time, x Survival rate, y The data were used to compute the equation of the least-squares line, which was ŷ = 100.90 9.21x. A newspaper article reported that "every minute spent waiting for paramedics to arrive with a defibrillator lowers the chance of survival by 10 percent." Is this statement consistent with the given least-squares line? Explain. O Since the slope of the least-squares line…arrow_forward
- Studies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered? The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitation center (in which cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes: Mean call-to-shock time, x 2 7 9 12 Survival rate, y 90 46 30 5 3 The data were used to compute the equation of the least-squares line, which was 3D 101.26 — 9.23х. A newspaper article reported that "every minute spent waiting for paramedics to arrive with a defibrillator lowers the chance of survival by 10 percent." Is this statement consistent with the given least-squares line? Explain. Since the slope of…arrow_forwardStudies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered? The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitation center (in which cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes. Mean call-to-shock time, x 2 6 7 9 12 Survival rate, y 92 44 31 4 3 n USE SALT (a) Construct a scatterplot for these data. y y y y 100 100 12 12• 10 80 10 80 8 8 60 60 6 40 40 4 4 20 20 20 40 60 80 100 6. 8 10 12 20 40 60 80 100 4 8 10 12 How would you describe the relationship between mean call-to-shock time and survival rate? O There is a strong positive relationship. The relationship is close to being…arrow_forwardStudies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered?The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitation center (in which cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes: Mean call-to-shock time, x 2 6 7 9 12 Survival rate, y 90 46 31 4 3 (a) Construct a scatterplot for these data. A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 13. The vertical axis is labeled "y" and has values from 0 to 100. 4 points are plotted in an almost straight line from approximately (2, 90) down and right to approximately (9, 5). 1 point is…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License