Video: SAT Practice Test 1 • Section 4 • Question 20

The given graphs show the results of a study that was conducted to test the hypothesis that men who are members of a gym have a lower body fat percentage than men who are not members of a gym. The study measured body fat percentage, rounded to the nearest percent, of 600 men who are members of a gym and 600 men who are not members of a gym. For the sake of this study, a “high” percentage of body fat is defined as a body fat percentage higher than 20%. Do these graphs provide strong evidence in support of the tested hypothesis?

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Video Transcript

The given graphs show the results of a study that was conducted to test the hypothesis that men who are members of a gym have a lower body fat percentage than men who are not members of a gym. The study measured body fat percentage, rounded to the nearest percent, of 600 men who are members of a gym and 600 men who are not members of a gym. For the sake of this study, a “high” percentage of body fat is defined as a body fat percentage higher than 20 percent. Do these graphs provide strong evidence in support of the tested hypothesis?

The top graph shows the percentage of 600 men who are members of a gym and the bottom graph shows the percentage of men who are not members of a gym. The hypothesis stated said that men who are members of a gym have a lower body fat percentage than men who are not members of a gym. We were also told that for this study a high percentage of body fat is defined as anything over 20 percent. The bars to the right-hand side of the orange line drawn on the graph are those men who had a body fat percentage over 20 percent.

Let’s first consider the top graph, men who are members of a gym. The bar representing body fat between 20 and 22 percent includes 15 percent of the population. The next bar also has a height of 15 percent. The third bar is slightly above five percent. We can estimate this to be six percent. The next bar is slightly below five percent. So we can estimate this to be four percent. The bar for 32 to 34 percent body fat is slightly higher than that of 26 to 28 percent. Therefore, we can estimate this to be seven percent of the population. Finally, the last bar is slightly above halfway between zero and five percent. Therefore, we can estimate this to be three percent.

Our next step is to add these six percentages: 15 percent, 15 percent, six percent, four percent, seven percent, and three percent. Adding these numbers gives us a total of 50 percent. Therefore, 50 percent of the men who are members of a gym have a high percentage of body fat. We now need to repeat this process with the men who are not members of a gym.

The six bars here correspond to 18 percent, eight percent, four percent, eight percent, 10 percent, and five percent. Once again, we need to add these six percentages. 18 plus eight plus four plus eight plus 10 plus five is equal to 53. Therefore, 53 percent of the men who are not members of a gym have a high percentage of body fat.

We were asked in the question to decide if the graphs provide strong evidence to support the hypothesis. As we have just worked out, the percentage of men who are members of a gym and percentage of men who are not members of a gym with a high percentage of body fat is very similar: 50 percent and 53 percent. We can therefore say that there is not strong evidence to support the hypothesis. However, in any question like this, we also need to give a reason.

A reason to support our answer in this case would be that the percentage of men who have a “high” body fat percentage is not significantly different between those who are and those who are not members of a gym. There is not enough evidence to suggest that the hypothesis that men who are members of a gym have a lower body fat percentage than men who are not from the data in the study. As with all hypotheses, we could test this further by looking at a larger sample of men.

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