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 7.7, 10.7, 3.6, 7.6, 1.8, 4.7, 4.3, 7.5, 7.7, 4.7 multivitamin 7.3, 5.6, 3.9, 7.7, 3.3, 3.0, 7.1, 4.1, 2.6, 5.1 Treated with vitamin C 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 μμ₂ between the mean recovery time when treated with multivitamins (μ₁) and the mean recovery time when treated with vitamin C only (₂). 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: X S

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, 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.

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.)

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.
Treated with
multivitamin
Days to recover from flu
7.7, 10.7, 3.6, 7.6, 1.8, 4.7, 4.3, 7.5, 7.7, 4.7
Treated with
vitamin C
Send data to calculator
7.3, 5.6, 3.9, 7.7, 3.3, 3.0, 7.1, 4.1, 2.6, 5.1
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 μ₁-μ₂ 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.
Lower limit:
Upper limit:
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.)
x

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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