Chapter 29.8, Problem 35SRE

(a)

To determine

Define the conclusion based on the provided information.

Explanation of Solution

Based on the given information, out of 12,866 men aged 35–57 at high risk of heart disease, 6,428 subjects were randomly assigned to the intervention group and the remaining 6,438 men were assigned to the control group.

Let x represent the intervention group and y represent the control group.

The following values are known:

$\begin{array}{l}\text{Sample mean,}\left(\overline{x}\right)=91.0\text{mm}\text{Hg}\\ \text{Sample standard deviation}\left(s_x\right)=7.6\text{mm}\text{Hg}\\ \text{Sample mean,}\left(\overline{y}\right)=90.9\text{mm}\text{Hg}\\ \text{Sample standard deviation}\left(s_y\right)=7.7\text{mm}\text{Hg}\end{array}$

It is observed that the sample means and sample standard deviations are approximately same in both groups. This indicates that the groups are approximately the same prior to the application of the treatments. Therefore, it may not be expected that any lurking variables affect the results of the experiment.

(b)

To determine

Describe the conclusion based on the provided information.

Explanation of Solution

Let x represent the intervention group and y represent the control group.

The following values are known:

$\begin{array}{l}\text{Sample mean,}\left(\overline{x}\right)=80.5\text{mm}\text{Hg}\\ \text{Sample standard deviation}\left(s_x\right)=7.9\text{mm}\text{Hg}\\ \text{Sample mean,}\left(\overline{y}\right)=83.6\text{mm}\text{Hg}\\ \text{Sample standard deviation}\left(s_y\right)=9.2\text{mm}\text{Hg}\end{array}$

It is observed that the sample means and sample standard deviations are both lower in the intervention group in comparison to the control group. This indicates that the treatment group appears to have been effective. The average blood pressure appears to have decreased in the intervention group, while the blood pressure was approximately the same in the two groups preceding to the treatments.

(c)

To determine

Delineate the conclusion based on the provided information.

Explanation of Solution

Let x represent the intervention group and y represent the control group.

The following values are known:

$\begin{array}{l}\text{Sample mean,}\left(\overline{x}\right)=253.8\text{mm}\text{Hg}\\ \text{Sample standard deviation}\left(s_x\right)=36.4\text{mm}\text{Hg}\\ \text{Sample mean,}\left(\overline{y}\right)=253.5\text{mm}\text{Hg}\\ \text{Sample standard deviation}\left(s_y\right)=36.8\text{mm}\text{Hg}\end{array}$

It is observed that the sample means and sample standard deviations are approximately the same in both groups. This indicates that the groups are approximately the same prior to the application of the treatments. Therefore, it may not be expected that any lurking variables affect the results of the experiment.

(d)

To determine

Label the conclusion based on the provided information.

Explanation of Solution

Let x represent the intervention group and y represent the control group.

The following values are known:

$\begin{array}{l}\text{Sample mean,}\left(\overline{x}\right)=235.5\text{mm}\text{Hg}\\ \text{Sample standard deviation}\left(s_x\right)=38.3\text{mm}\text{Hg}\\ \text{Sample mean,}\left(\overline{y}\right)=240.3\text{mm}\text{Hg}\\ \text{Sample standard deviation}\left(s_y\right)=39.9\text{mm}\text{Hg}\end{array}$

It is observed that the sample means and sample standard deviations are both lower in the intervention group in comparison to the control group. This indicates that the treatment group appears to have a decreased serum cholesterol level. The average serum cholesterol level appears to have decreased in the intervention group, while the serum cholesterol level was approximately the same in the two groups preceding to the treatments.

(e)

To determine

Explain the conclusion based on the provided information.

Explanation of Solution

Let x represent the intervention group and y represent the control group.

The following values are known:

$\begin{array}{l}\text{Sample proportion,}\left({\widehat{p}}_x\right)=0.593\left(=\frac{59.3}{100}\right)\\ \text{Sample proportion,}\left({\widehat{p}}_x\right)=0.59\left(=\frac{59}{100}\right)\end{array}$

It is observed that the sample proportion of smoking is approximately the same in both groups. This indicates that the groups are approximately the same prior to the application of treatments. Therefore, it may not be expected that any lurking variables affect the results of the experiment.

(f)

To determine

Explain the conclusion based on the provided information.

Explanation of Solution

Let x represent the intervention group and y represent the control group.

The following values are known:

$\begin{array}{l}\text{Sample proportion,}\left({\widehat{p}}_x\right)=0.323\left(=\frac{32.3}{100}\right)\\ \text{Sample proportion,}\left({\widehat{p}}_x\right)=0.456\left(=\frac{45.6}{100}\right)\end{array}$

It is observed that the sample proportion of smoking is lower in the interval group in comparison with the control group. This indicates that the treatment group appears to have decreased the likelihood to smoke as the proportion of smoking appears to have reduced in the intervention group. On the other hand, the proportion of smoking was approximately the same in the two groups preceding to the treatment.

(g)

To determine

Elucidate the conclusion based on the provided information.

Explanation of Solution

From the information provided, 211 men died after 6 years in the intervention group and 219 men died after 6 years in the control.

Since the difference between two groups is 8 $\left(=219-211\right)$ deaths, it may be concluded that approximately the same number of deaths occurred between the two treatment groups.

Therefore, this indicates that the treatment appears to have no effect on the death rate as the number of deaths remained approximately the same in the two treatment groups.