1. A study was conducted by a group of neurosurgeons. They compared a dynamic system (Z-plate) and a static system (ALPS plate) in terms of the number of acute postop- erative days in the hospital spent by the patients. The descriptive statistics for these data are as follows: for 14 patients with dynamic system, the sample mean number of acute postoperative days was 7.36 with standard deviation of 1.22; for 6 patients with static system the sample mean number of acute postoperative days was 10.5 with sample standard deviation of 4.59. Assume that the numbers of acute postoperative days in both populations are normally distributed. We wish to estimate μ1 − μ2 with a 99 percent confidence interval. a. Unknown population variances can be assumed equal i. True ii. False b. Degrees of Freedom i. 18 ii. 20 iii. 2.553 iv. 2.878 c. What is the t−value to be used in calculation of margin of error? i. 3.365 ii. 4.032 iii. 2.553 iv. 2.878 d. Margin of Error i. 4.86 ii. 5.47 iii. 6.40 iv. 7.67 e. Confidence Interval i. (−10.81,4.53) ii. (−9.54,3.26) iii. (−8.00,1.72) iv. (−8.61,2.33) f. Based on your interval in part (e), we can state with 99 percent confidence that the average numbers of acute postoperative days in two populations i. Are significantly different ii. Are not significantly different

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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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1. A study was conducted by a group of neurosurgeons. They compared a dynamic system (Z-plate) and a static system (ALPS plate) in terms of the number of acute postop- erative days in the hospital spent by the patients. The descriptive statistics for these data are as follows: for 14 patients with dynamic system, the sample mean number of acute postoperative days was 7.36 with standard deviation of 1.22; for 6 patients with static system the sample mean number of acute postoperative days was 10.5 with sample standard deviation of 4.59. Assume that the numbers of acute postoperative days in both populations are normally distributed. We wish to estimate μ1 − μ2 with a 99 percent confidence interval.

a. Unknown population variances can be assumed equal

i. True

ii. False

b. Degrees of Freedom

i. 18

ii. 20

iii. 2.553

iv. 2.878

c. What is the t−value to be used in calculation of margin of error?

i. 3.365

ii. 4.032

iii. 2.553

iv. 2.878

d. Margin of Error

i. 4.86

ii. 5.47

iii. 6.40

iv. 7.67

e. Confidence Interval

i. (−10.81,4.53)

ii. (−9.54,3.26)

iii. (−8.00,1.72)

iv. (−8.61,2.33)

f. Based on your interval in part (e), we can state with 99 percent confidence that the average numbers of acute postoperative days in two populations

i. Are significantly different

ii. Are not significantly different

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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