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?

Question

anonymous · Answer

attachment

anonymous · Answer

A.  The difference in the means is significant because a difference of 2 is very likely.
B.  The difference in the means is significant because a difference of 2 is not very likely.
C.  The difference in the means is not significant because a difference of 2 is not very likely.
D.  The difference in the means is not significant because a difference of 2 is very likely.

anonymous · Answer

@jim_thompson5910 
Can you look at this real quick?

anonymous · Answer

I think it is A or C.

jim_thompson5910 · Answer

ok let me read this over

one sec

jim_thompson5910 · Answer

Null Hypothesis: 
H0: mu1 - mu2 = 2

Alternate Hypothesis
H1: mu1 - mu2 =/= 2

If we tested the null hypothesis, we would assume the null is true for the time being. After doing the test, if we find the difference of 2 to be very unlikely, then we reject the null. The more unlikely 2 is to show up, the more statistically significant the conclusion (basically the more certain you are of the decision)

anonymous · Answer

So it would be C?

jim_thompson5910 · Answer

so if we're focusing on +2, we see that it shows up only 1 time out of 54 times

1/54 = 0.0185 which is roughly 1.85%

this is less than the default 5% threshold, making it statistically significant

jim_thompson5910 · Answer

so to sum things up

the conclusion of rejecting the null IS significant since 2 barely shows up
the difference of 2 is not very likely

anonymous · Answer

So B,  The difference in the means is significant because a difference of 2 is not very likely.?

jim_thompson5910 · Answer

yes, making us reject the null in favor of the alternate

anonymous · Answer

Ok, thank you!

anonymous · Answer

@jim_thompson5910  omg lol you answered this ahah