Chapter 5.2, Problem 60E

(a)

To determine

Complete randomized design for the experiment.

Explanation of Solution

A completely randomized experiment allocates all participants of the group at random.

Let us allocate a unique number to 1649 women each between 1 and 1649 (including both the numbers).

Draw randomly 825 unique numbers between 1 and 1649 (including both the numbers), that can be done by using a random digits table or technology, or by using slips of papers.

According to 825 selected integers, the corresponding 825 women will be assigned to the Strontium ranelate treatment, whereas the remaining 824 women will be assigned to the placebo treatment.

(b)

To determine

Importance of keeping the calcium supplements and medical care the same for all the women in the experiment.

Explanation of Solution

Two variables are confounded when their effects cannot be distinguished from each other on a response variable.

In the experiment, if we do not keep the calcium supplements and the medical care the same for all women, we cannot then be sure that the differences amongthe treatments are due to treatment, calcium supplements or medical care.

That means the medical care and the calcium supplements will confound the results, i.e., we will not be able to distinguish their effects on the results from the treatments effects.

Furthermore, because of the confusion, we will then be unable to prove any causation.

(c)

To determine

Meaning of the statement to someone who knows little statistics.

Explanation of Solution

“Statistically significant” means that the differences have been so large that they are unlikely to be due to chance.

“The women who took strontium ranelate had statistically significantly fewer new fractures, on average than the women who took a placebo over a 3-year period”.

This means that women who took strontium ranelate had on average so many fewer new fractions compared to women who took placebo and that is unlikely to be due to chance.