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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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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

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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