1. A study was conducted to testthe hypothesis that Vitamin C significantly redu

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1. A study was conducted to testthe hypothesis that Vitamin C significantly reduces incidence ofthe common cold. 11 of the study participants were randomlyallocated to a treatment group
which received daily Vitamin C capsules. Another 11 participantswere randomly allocated to
the control group which received daily placebo capsules. Boththe participants and the nurses
administering the capsules did not know which goup individualparticipants belonged to.
The number of colds caught over a 12-month period by eachparticipant are shown below.
Assume the data for both groups are random samples from independentnormally distributed populations.

Number of Colds in 12-month Period

Treatment Group: 4 0 3 4 4 2 3 4 2 3 4
Control Group:      7 8 6 5 6 4 7 5 5 6 4

a.) Compute a 95% confidence interval for the difference inmeans between
the Treatment group and the Control group.

b.) Which of the following statements is true?

       1. Confidence intervalcomputed above contains zero, so treatment group mean does notequal control group mean.
       2. Confidence intervalcomputed above contains zero, so treatment group mean equalscontrol group mean.
       3. Entire confidence intervalcomputed above is less than zero, so treatment group mean issignificantly greater than control group mean.
       4. Entire confidence intervalcomputed above is less than zero, so treatment group mean issignificantly smaller than control group mean.
       5. Entire confidence intervalcomputed above is greater than zero, so treatment group mean issignificantly greater than control group mean.
       6. Entire confidence intervalcomputed above is greater than zero, so treatment group mean issignificantly less than control group mean.

c.) Using the data above, test the hypothesis, at = .05,that on average the Treatment group had fewer colds.
Once again assume the data for both groups to be random samplesfrom independent normally distributed populations.

d.) What is the value of your test statistic ?
e.) How many degrees of freedom does it have ?

f.) What is the pValue for the test ?

2. Again use data from problem 1 above to test the hypothesis,at = .05,
that on average the Treatment group had fewer colds. Thistime assume
data for both groups are random samples from normally distributedpopulations
with equal variance.

a.) Compute a 95% confidence interval for the differencein means between
the Treatment group, T, and the Control group,C.

b.) Test the hypothesis, at = .05, that on averagethe Treatment group had fewer colds.
Once again assume the data for both groups to be random samplesfrom independent normally
distributed populations. What is the value of your teststatistic ?

c.) How many degrees of freedom does it have ?

d.) What is the pValue for the test ?

3. Suppose that each participant in the Treatment group inproblem 1 is in
someway paired with a corresponding member of the Control group,that
is, Treatment group Subject 1 is paired with Control group Subject1
and so on.

a.) Test the hypothesis, at = .05, that on average theTreatment
group had fewer colds. What is the value of your test statistic?

b.) How many degrees of freedom does the test statistic in(a.) have ?

c.) What is the pValue for the test outlined in (a.) ?

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