Homework Help is Here – Start Your Trial Now!
Math
Statistics
rataily 7.15 Suppose we eventually plan to accumulate 50 MI cases during the period 2010-2015. Assume that the 24-hour case-fatality rate is truly 20% during this period. How much power would such a study have in distinguishing between case-fatality rates in 2000 and 2010-2015 if a two-sided test with significance level .05 is planned?

rataily 7.15 Suppose we eventually plan to accumulate 50 MI cases during the period 2010-2015. Assume that the 24-hour case-fatality rate is truly 20% during this period. How much power would such a study have in distinguishing between case-fatality rates in 2000 and 2010-2015 if a two-sided test with significance level .05 is planned?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
**PROBLEMS** **Renal Disease** The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. **7.1** If the mean and standard deviation of serum creatinine in the general population are 1.0 and 0.4 mg/dL, respectively, then, using a significance level of .05, test whether the mean serum-creatinine level in this group is different from that of the general population. **7.2** What is the p-value for the test? **7.3** Suppose the sample standard deviation of serum creatinine in Problem 7.1 is 0.6 mg/dL. Assume that the standard deviation of serum creatinine is not known, and perform the hypothesis test in Problem 7.1. Report a p-value. **7.4** Compute a two-sided 95% CI for the true mean serum-creatinine level in Problem 7.3. **7.5** How does your answer to Problem 7.4 relate to your answer to Problem 7.3? **7.6** Suppose \( \frac{\bar{X} - \mu_0}{s/\sqrt{n}} = -1.52 \) and a one-sample t-test is performed based on seven subjects. What is the two-tailed p-value? **7.7** Use a computer program to compute the probability that a t-distribution with 36 df exceeds 2.5. **7.8** Use a computer program to compute the lower 10th percentile of a t-distribution with 54 df. **Diabetes** Plasma-glucose levels are used to determine the presence of diabetes. Suppose the mean in (plasma-glucose) concentration (mg/dL) in 35- to 44-year-olds is 4.86 with standard deviation = 0.54. A study of 100 sedentary people in this age group is planned to test whether they have a higher or lower level of plasma glucose than the general population. **7.9** If the expected difference is 0.10 in units, then what is the power of such a study if a two-sided test is to be used with \( \alpha = 0.05 \)? **7.10** Answer Problem 7.9 if the expected difference is 0
Transcribed Image Text:**PROBLEMS** **Renal Disease** The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. **7.1** If the mean and standard deviation of serum creatinine in the general population are 1.0 and 0.4 mg/dL, respectively, then, using a significance level of .05, test whether the mean serum-creatinine level in this group is different from that of the general population. **7.2** What is the p-value for the test? **7.3** Suppose the sample standard deviation of serum creatinine in Problem 7.1 is 0.6 mg/dL. Assume that the standard deviation of serum creatinine is not known, and perform the hypothesis test in Problem 7.1. Report a p-value. **7.4** Compute a two-sided 95% CI for the true mean serum-creatinine level in Problem 7.3. **7.5** How does your answer to Problem 7.4 relate to your answer to Problem 7.3? **7.6** Suppose \( \frac{\bar{X} - \mu_0}{s/\sqrt{n}} = -1.52 \) and a one-sample t-test is performed based on seven subjects. What is the two-tailed p-value? **7.7** Use a computer program to compute the probability that a t-distribution with 36 df exceeds 2.5. **7.8** Use a computer program to compute the lower 10th percentile of a t-distribution with 54 df. **Diabetes** Plasma-glucose levels are used to determine the presence of diabetes. Suppose the mean in (plasma-glucose) concentration (mg/dL) in 35- to 44-year-olds is 4.86 with standard deviation = 0.54. A study of 100 sedentary people in this age group is planned to test whether they have a higher or lower level of plasma glucose than the general population. **7.9** If the expected difference is 0.10 in units, then what is the power of such a study if a two-sided test is to be used with \( \alpha = 0.05 \)? **7.10** Answer Problem 7.9 if the expected difference is 0
**Expert Solutions / Fundamentals of Biostatistics** **Exercise 15** Chapter 7, Page 269 **Fundamentals of Biostatistics** ISBN: 9781305268920 [Table of contents](#) --- **Solution** *Verified* **Step 1** Use the Equation 7.20 (b) on p.237 of the book. First, we need to calculate \( sd = \sqrt{0.005(1 - 0.005)} = 0.71 \). \[ \text{Power} = \Phi\left(-z_{1-\alpha/2} + \frac{(0.20 - 0.005) \cdot \sqrt{50}}{0.71}\right) \] \[ = \Phi(-1.96 + 1.94) = \Phi(-0.018) = 0.494 \] Hence, the chance of getting a significant result with a two-tailed test is 49.4%. **Result** 0.494 --- **Note:** The text includes handwritten inquiries asking for clarification on finding the standard deviation and the formula used.
Transcribed Image Text:**Expert Solutions / Fundamentals of Biostatistics** **Exercise 15** Chapter 7, Page 269 **Fundamentals of Biostatistics** ISBN: 9781305268920 [Table of contents](#) --- **Solution** *Verified* **Step 1** Use the Equation 7.20 (b) on p.237 of the book. First, we need to calculate \( sd = \sqrt{0.005(1 - 0.005)} = 0.71 \). \[ \text{Power} = \Phi\left(-z_{1-\alpha/2} + \frac{(0.20 - 0.005) \cdot \sqrt{50}}{0.71}\right) \] \[ = \Phi(-1.96 + 1.94) = \Phi(-0.018) = 0.494 \] Hence, the chance of getting a significant result with a two-tailed test is 49.4%. **Result** 0.494 --- **Note:** The text includes handwritten inquiries asking for clarification on finding the standard deviation and the formula used.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS