A random selection of volunteers at a research institute has been exposed to a weak flu virus. After the volunteers began to have flu symptoms, 10 of them were given multivitamin tablets daily that contained 1 gram of vitamin C and 3 grams of various other vitamins and minerals. The remaining 10 volunteers were given tablets containing 4 grams of vitamin C only. For each individual, the length of time taken to recover from the flu was recorded. At the end of the experiment the following data were obtained. Days to recover from flu Treated with multivitamin 5.3 , 4.1 , 2.8 , 6.0 , 4.4 , 7.9 , 6.5 , 8.4 , 7.9 , 3.1 Treated with vitamin C 3.5 , 3.6 , 4.9 , 4.0 , 3.9 , 4.5 , 4.8 , 3.7 , 5.3 , 1.4 Send data to calculator Send data to Excel Suppose that it is known that the population standard deviation of recovery time from the flu is 1.8 days when treated with multivitamins and that the population standard deviation of recovery time from the flu is 1.5 days when treated with vitamin C tablets. Suppose also that both populations are approximately normally distributed. Construct a 95% confidence interval for the difference −μ1μ2 between the mean recovery time when treated with multivitamins ( μ1 ) and the mean recovery time when treated with vitamin C only ( μ2 ). Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list of formulas.) Lower limit: Upper limit:

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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A random selection of volunteers at a research institute has been exposed to a weak flu virus. After the volunteers began to have flu symptoms,

of them were given multivitamin tablets daily that contained

gram of vitamin C and

grams of various other vitamins and minerals. The remaining

volunteers were given tablets containing

grams of vitamin C only. For each individual, the length of time taken to recover from the flu was recorded. At the end of the experiment the following data were obtained.

	Days to recover from flu
Treated with multivitamin	5.3 , 4.1 , 2.8 , 6.0 , 4.4 , 7.9 , 6.5 , 8.4 , 7.9 , 3.1
Treated with vitamin C	3.5 , 3.6 , 4.9 , 4.0 , 3.9 , 4.5 , 4.8 , 3.7 , 5.3 , 1.4

Send data to calculator

Send data to Excel

Suppose that it is known that the population standard deviation of recovery time from the flu is

1.8

days when treated with multivitamins and that the population standard deviation of recovery time from the flu is

1.5

days when treated with vitamin C tablets. Suppose also that both populations are approximately normally distributed. Construct a

95%

confidence interval for the difference

−μ1μ2

between the mean recovery time when treated with multivitamins (

μ1

) and the mean recovery time when treated with vitamin C only (

μ2

). Then find the lower limit and upper limit of the

95%

confidence interval.

Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list of formulas.)

Lower limit:
Upper limit:

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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