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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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
---
**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeadb183-1175-48ee-be1d-be4cbd36e1e9%2F64e77d44-20e0-4a96-9d01-d1a340dee16b%2Frjhgdw_processed.jpeg&w=3840&q=75)
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.
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