## Related questions with answers

Many observational studies conclude that low-fat diets protect against cancer and cardiovascular "events" (heart attacks, stroke, and so forth). Experimental results, however, are generally negative. In 2006, the Women's Health Initiative (WHI) published its results. This was a large-scale randomized trial on women who had reached menopause. As one part of the study, 48,835 women were randomized: 19,541 were assigned to the treatment group and put on a low-fat diet. The other 29,294 women were assigned to the control group and ate as they normally would. Subjects were followed for 8 years. Among other things, the investigators found that 1,357 women on the low-fat diet experienced at least one cardiovascular event, compared to 2,088 in the control group. can the difference between the two groups be explained by chance? What do you conclude about the effect of the low-fat diet?

Solution

Verified1,357 of the 19,541 women in the treatment group had at least one cardiovascular event, while 2,088 of the 29,294 women in the control group had at least one cardiovascular event.

$\begin{align*} \text{Percentage A}&=\frac{1357}{19541}\approx 0.0694=6.94\% \\ \text{Percentage B}&=\frac{2088}{29294}\approx 0.0713=7.13\% \\ \text{Sample size A}&=19,541 \\ \text{Sample size B}&=29,294 \end{align*}$

The box corresponding treatment group contains a ticket per woman in the treatment group, where the value on the ticket is a 1 when she had a cardiovascular event and otherwise the value on the ticket is 0. The box corresponding to the control group contains a ticket per woman in the control group, where the value on the ticket is a 1 when she had a cardiovascular and otherwise the value on the ticket is 0.

The null hypothesis states that the two boxes contains have the same percentage, while the alternative hypothesis states that the percentages are different.

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