Construct a 90% 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 90% 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,
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 |
3.2
7.3
8.4
6.1
2.5
6.7
6.3
3.7
7.0
7.7
9.1
9.9
9.0
2.6
2.0
5.1
5.7
2.5
2.9
4.5
|
| Treated with vitamin C |
2.7
5.3
3.7
5.5
4.5
3.8
7.6
5.3
3.6
5.2
2.3
4.7
3.6
5.2
2.3
7.1
3.3
6.1
7.9
4.2
|
|
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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
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.
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.)
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