Question

Lars wants to know if warming up will help runners sprint faster. Twenty-four track and field athletes volunteered to participate in his study. He randomly assigns 12 athletes to warm-up for 10 minutes. All 24 participants sprint the same distance. He calculates the mean for each group and determines that the mean for the warm-up group was 7.8 seconds and the mean for the other group was 9.8 seconds. To test the difference of means, he re-randomized the data 54 times and the differences are plotted in the dot plot below. What can Lars conclude from her study?

Answer 1

The difference in the means is significant because a difference of 2 is very likely.
The difference in the means is significant because a difference of 2 is not very likely.
The difference in the means is not significant because a difference of 2 is not very likely.
The difference in the means is not significant because a difference of 2 is very likely.

Answer 2

@amistre64 @phi @dtan5457

Answer 3

@Hero

Answer 4

@perl

Answer 5

based on the graph, how many points are less than or equal to -2 or >= 2 ?

Answer 6

0 for less than or equal to -2 and 9 for greater than 2

Answer 7

oh points thought you were talking about the diamonds over the points

Answer 8

Yes, the diamonds over the points

Answer 9

so im right? with 0 and 9

Answer 10

I see 6 at -2 and 3 at -2.5 and 1 at +2
that adds up to 9 less than or equal to -2 and 1 point >= +2
so 10 points all together. They say there are 54 points
so is the chance of a getting a difference of 2 large or small ?

Answer 11

oh i get what youre saying now

Answer 12

i would think large

Answer 13

10 out of 54 is large ?

Answer 14

i was debating that, no

Answer 15

so that cuts out A and D

Answer 16

would it be c? don't really get what it means by difference in mean

Answer 17

I guess we have to decide what is likely or not likely. usually we use 5% chance as a cut off. Here there is 18.5% chance we will get a difference >= 2 due to chance.

Answer 18

that's what i was having a problem with before, i don't know if that would be considered likely or not. close to a 1/5 chance, shouldn't that be a matter of opinion?

Answer 19

I am having a hard time deciphering
difference of 2 is very likely
versus
difference of 2 is not very likely

I may be wrong on this, but I would go with significant because difference of 2 is likely
but I would not hold my breath that is correct.