a. Construct a 95% confidence interval for the true mean decrease in cholesterol levels for people who take the drug treatment for 3 months. For credit, your work must include a filled out formula for your confidence interval.b. After the study was completed, the pharmaceutical company claims that the cholesterol levels have decreased. Does this confidence interval contradict this claim? Explain why. 14. A pharmaceutical company is testing a new drug that is supposed to lower cholesterol levels. Ten volunteersparticipate in a 3 month study that compares their cholesterol level before and after the 3 month treatment. Theresults are below. Units of measure are mg/dL.Initial Level210 200 215 194 206 221 203 189 208 211Level after 3 months 201 195 208 197 200 203 190 188 210 210

(a) The objective is to construct a 95% confidence interval for the true mean decrease in cholesterol levels for people who take the drug treatment for 3 months. The formula to compute the confidence interval is: C.I=d¯±t*sdn where, d¯ is the mean of the differences sd is the standard deviation of the differences t* is the t critical value. Required calculations: Before After d=After-Before 210 201 -9 200 195 -5 215 208 -7 194 197 3 206 200 -6 221 203 -18 203 190 -13 189 188 -1 208 210 2 211 210 -1 ∑di=-55 Mean of the differences is: d¯=∑din=-5510=-5.5 Standard deviation of the differences is computed as follows: sd=∑di-d¯2n-1=-9-(-5.5)2+-5-(-5.5)2+-7-(-5.5)2+.....+-1-(-5.5)210-1=6.637436 Using the t-table, t critical value at degrees of freedom df=10-1=9 and 95% confidence level is: 2.262 Substitute the values in the formula: C.I=d¯±t*sdn=-5.5±2.2626.63743610=-5.5±4.747805805=-5.5-4.747805805, -5.5+4.747805805≈-10.25, -0.75 Thus, the 95% confidence interval for the true mean decrease in cholesterol levels for people who take the drug treatment for 3 months is (-10.25, -0.75). (b) Given that, after the study was completed, the pharmaceutical company claims that the cholesterol levels have decreased. The confidence interval obtained in part (a) does not contradict this claim, because the confidence interval includes only negative values (does not include zero). Thus, it can be concluded that there is a true mean decrease in cholesterol levels for people who take the drug treatment for 3 months (i.e., After group).

Answered: 14. A pharmaceutical company is testing…

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

Related questions

Question

a. Construct a 95% confidence interval for the true mean decrease in cholesterol levels for people who take the drug treatment for 3 months. For credit, your work must include a filled out formula for your confidence interval.

b. After the study was completed, the pharmaceutical company claims that the cholesterol levels have decreased. Does this confidence interval contradict this claim? Explain why.

14. A pharmaceutical company is testing a new drug that is supposed to lower cholesterol levels. Ten volunteers
participate in a 3 month study that compares their cholesterol level before and after the 3 month treatment. The
results are below. Units of measure are mg/dL.
Initial Level
210 200 215 194 206 221 203 189 208 211
Level after 3 months 201 195 208 197 200 203 190 188 210 210

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 + ...

Expert Solution