Concept explainers
(a)
To explain: the 95 percent confidence interval for the percent of individuals taking medicine A that can get relief from this form of joint pain.
(a)
Answer to Problem 27E
(0.6698, 0.8302)
Explanation of Solution
Given:
Of the 112 individuals who received treatment A in the community, 84 said that this pain reliever was successful. With
Formula used:
For the confidence interval
Calculation:
The standard error is
For a 95% confidence level,
therefore, the 95 percent confidence interval is
If the observed proportion is 75 percent, then there are 95 percent sure that treatment A will be successful for between 67 percent and 83 percent of the population proportion of individuals who have complained of a certain form of joint pain.
(b)
To explain: the 95 percent confidence interval for the percent of individuals taking medicine B that can get relief from this form of joint pain.
(b)
Answer to Problem 27E
(0.5192, 0.7031)
Explanation of Solution
Given:
Of the 108 individuals in the group receiving treatment B, 66 indicated that this pain relief was successful with
Formula used:
For the confidence interval
Calculation:
Standard error is
For a 95% confidence level,
Therefore, the 95 percent confidence interval is
If the observed proportion is 61 percent, then there are 95 percent sure that treatment B will be successful between 51.9 percent and 70.3 percent of the population proportion of individuals who have complained of a certain type of joint pain.
(c)
To Explain: about the overlap of interval A and B and about the comparative effectiveness of this medications.
(c)
Explanation of Solution
Yes, the A and B intervals overlap. This may mean that the proportion of people who have complained of a certain type of joint pain in the population would find treatment A successful and medication B successful.
(d)
To explain: the 95 % confidence interval for the proportion difference of individuals who will find this drug effective.
(d)
Answer to Problem 27E
(0.0169, 0.2609)
Explanation of Solution
Given:
Formula used:
For the confidence interval
Calculation:
Observed proportions are
Estimating the standard deviation
For a 95% confidence level,
So, the 95% confidence interval is
95 percent confidence interval for the proportion difference of people who received treatment A and said that this pain reliever was beneficial and that this pain reliever was beneficial for people who received treatment B and said it was effective (0.0169. 0.2609). This indicates that 1.7% to 26% more users explore that treatment A is safe.
(e)
To Explain: about the including the zero in the interval and the meaning of this.
(e)
Explanation of Solution
No, 0.0 is not included in this interval. This means 0 is not the difference 's probable value. it might assume that the efficacy of treatment A and treatment B for joint pain differ.
(f)
To Explain: the reason that the results in part (c) and (e) looks contradictory, if want to compare the effectiveness of these two pain relievers and the find the correct approach.
(f)
Explanation of Solution
There is required to need to estimate the standard deviation of the difference if there is required to estimate the difference in the proportions of individuals that will find these treatments successful. The difference cannot be explained by two separate confidence intervals. If there is required to evaluate the efficacy of these two pain relievers, the two-sample method is the right strategy.
Chapter 22 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
Additional Math Textbook Solutions
Statistics for Psychology
Basic Business Statistics, Student Value Edition (13th Edition)
Basic Business Statistics, Student Value Edition
Essentials of Statistics (6th Edition)
- 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