Question

Treating low bone density Fractures of the spine are common and serious

among women with advanced osteoporosis (low mineral density in the bones). Can taking

strontium ranelate help? A large medical trial was conducted to investigate this question.

Researchers recruited $1649$women with osteoporosis who had previously had at least one

fracture for an experiment. The women were assigned to take either strontium ranelate or a

placebo each day. All the women were taking calcium supplements and receiving standard

medical care. One response variable was the number of new fractures over $3$years.

a. Describe a completely randomized design for this experiment.

b. Explain why it is important to keep the calcium supplements and medical care the same

for all the women in the experiment.

c. 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. Explain

what this means to someone who knows little statistics.

Short answer

a. We can make a completely randomized design by assigning a unique no. between $1and1649$

to each of $1649$women.

b. Calcium supplements and medical care will confound the results if we do not keep them the same for all the women in the experiment.

c. On average, the women who took strontium ranelate had fewer new fractures than the women who took a placebo, indicating that the large difference is unlikely to be due to chance.

Step-by-step solution

Part (a): Step 1: Given information

We have been given that a large medical trial was conducted to investigate this question.

Researchers recruited $1649$women with osteoporosis and the women were assigned to take either strontium ranelate or a placebo each day.

We need to describe a completely randomized design for this experiment

Part (a): Step 2: Explanation

In a completely randomized experiment, let us assign a unique number between $1and1649$to each of $1649$woman.

We have to randomly draw $825$unique numbers between $1and1649$.

Now the $825$corresponding women will be assigned to strontium ranelate and the remaining $824$women are assigned to placebo treatment.

Part (b): Step 1: Given information

We have been given that a large medical trial was conducted to investigate this question.

Researchers recruited $1649$women with osteoporosis and the women were assigned to take either strontium ranelate or a placebo each day.

We need to find why it is important to keep the calcium supplements and medical care the same

for all the women in the experiment.

Part (b): step 2: Explanation

If we do not keep the calcium supplements and medical care the same for all the women in the experiment then we will not be able to see whether the differences in the treatments are due to treatment or due to calcium supplements or medical care. We will not be able to distinguish their effect on the results.

Part (c): Step 1: Given information

We have been given that a large medical trial was conducted to investigate this question.

Researchers recruited $1649$women with osteoporosis and the women were assigned to take either strontium ranelate or a placebo each day.

We need to find out why the women who took strontium ranelate had statistically significantly fewer new fractures, on average than the women who took a placebo.

Part (c): Step 2: Explanation

''Statistically significant'' mean differences were so large that the differences are unlikely due to chance.

the women who took strontium ranelate had statistically significantly fewer new fractures, on average than the women who took a placebo, that is unlikely that the large amount is due to chance.