Erin wants to know if warming up will help runners sprint faster. Twenty-six track and field athletes volunteered to participate in her study. She randomly assigns 13 athletes to warm-up for 10 minutes. All 26 participants sprint the same distance. She calculates the mean for each group and determines that the mean for the warm-up group was 10.9 seconds, and the mean for the other group was 12.9 seconds. To test the difference of means she re-randomized the data 54 times, and the differences are plotted in the dot plot below. What can Erin conclude from her study?

A dot plot is shown labeled from negative 2.5 to positive 2. Above the negative 2.5 are 3 dots. Above the negative 2 are 6 dots. Above the negative 1.5 are 9 dots. Above the negative 1 are 12 dots. Above the negative 0.5 are 6 dots. Above the 0.0 are 4 dots. Above the 0.5 are 3 dots. Above the 1.0 are 7 dots. Above the 1.5 are 3 dots. Above the 2.0 is 1 dot.

The difference in the means is not significant because a difference of 1 is very likely is true option describing this group of 20 who sprints in two different groups each having 10 members.

What is mean?

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations.

There are two groups, each consisting of 10 members.

Group A which consists of 10 members, has warmed up for 10 minutes.

Warming up before running will make the runners run for a longer time and run fast if they are running for a shorter duration of time.

Now,

Mean for the warm-up group = 10.9 seconds

Mean for other groups = 11.9 seconds

The difference in mean of the two groups = 11.9-10.9 = 1

Now, To test the difference in means she re-randomized the data 54 times, and the differences are plotted in the dot plot below.

As, the difference of mean = 1, which occurs for a maximum of 12 times.

As the difference in means is not too large.

So, in option A The difference in the means is not significant because a difference of 1 is very likely is true option describing this group of 20 who sprints in two different groups each having 10 members.

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