Basic Statistics

PROBLEMS 91

In this example, the pairing of the weights on the same adult was a natural outcome
of how the measurements were taken; it is obvious that the paired comparison is the
one to use. When artificial pairs are created in clinical trials to assure that the treatment
and control groups are similar in, say, age and gender, the reduction in the length of
the confidence interval is often not great. Since patients usually enter the trial one
at a time, the investigator may often be unable to find a close match for a patient
already entered. Random assignment is strongly recommended for clinical trials. In
casekontrol studies, since random assignment is not possible, pairing is often done
not so much to reduce the size of the confidence interval as to ensure that the cases
and controls are similar on some factors that might affect the outcome. The decision
to pair or not to pair often depends on the type of research study being done and
whether it is a simple process to find pairs.

PROBLEMS

7.1

7.2

7.3

7.4

The time taken for cessation of bleeding was recorded for a large number of

persons whose fingers had been pricked. The mean time was found to be

1.407 min and the standard deviation was .588 min. In an effort to determine

whether pressure applied to the upper arm increases bleeding time, six persons

had pressure equal to 20 mmHg applied to their upper arms and had their fingers

pricked. For these six persons, the times taken for bleeding to stop were 1.15,

1.75, 1.32, 1.28, 1.39, and 2.50min. Give a 95% confidence interval for the

mean bleeding time under pressure for the six persons and draw some conclusion

as to whether pressure increases bleeding time.

Make a 95% confidence interval for the mean of the cholesterol-level population

using each of the samples gathered in Exercise 2.1, assuming that you know

that GT = 45.3 mg/100mL (three confidence intervals, one for each sample).

Gather all the confidence intervals that the class constructed in Exercise 7.2,

and make a graph plotting each interval as a vertical line. The population mean

of the 98 cholesterol measurements is 279.5 mgA00 mL. How many intervals

cross a horizontal line p = 279.5 mg/100 rnL? About how many would you

expect to cross a line p = 279.5 mg/100mL?

Mice from 12 litters were weighed when 4 months old, with one male and one

female weighed from each litter. Weight in grams was recorded as follows:

Litter Number Male Female

1 26.0 16.5

2 20.0 17.0

3 18.0 16.0

4 28.5 21.0

5 23.5 23.0

6 20.0 19.5

7 22.5 18.0

8 24.0 18.5

9 24.0 20.0

10 25.0 28.0

11 23.5 19.5

12 24.0 20.5