Question

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 , , , , , , , , , Treated with vitamin C , , , , , , , , , Suppose that it is known that the population standard deviation of recovery time from the flu is days when treated with multivitamins and that the population standard deviation of recovery time from the flu is days when treated with vitamin C tablets. Suppose also that both populations are approximately normally distributed. Construct a confidence interval for the difference between the mean recovery time when treated with multivitamins () and the mean recovery time when treated with vitamin C only (). Then find the lower limit and upper limit of the confidence interval.

Answer 1

The confidence interval is given as lower interval is -0.77 while The upper interval is 1.67

How to solve for the confidence interval

Multivitamin treatment

n1 is 10

σ1 = 1.8

x21 = 5

vitamin C treatment

n2 = 10

σ2 = 1.5

x2 = 4.55

zα/2 = 1.645

The formula for the confidence interval is given as

(x1 - x2) ± zα/2$\sqrt{\frac{sd1^2}{n1}+\frac{sd2^2}{n2} }$

When we input the values we have above we would have

CI = (-0.7688550 , 1.668855 )

The the lower interval is -0.77

The upper interval is 1.67

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Complete question

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

2.4, 6.4, 9.1, 4.1, 4.6, 6.4, 6.4, 3.2, 6.9, 0.5

Treated with Vitamin C

5.2, 3, 3.6, 5.5, 7.5, 6.7, 1.3, 1.9, 5.3, 5.5

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 90% confidence interval for the difference µµ₂ between the mean recovery time when treated with

multivitamins (μ,) and the mean recovery time when treated with vitamin C only (H2). Then complete the table below.

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.)

What is the lower limit of the 90% confidence interval?

What is the upper limit of the 90% confidence interval?