Help with probability, please?

Question

anonymous · Answer

@jim_thompson5910 @Nnesha @nincompoop

anonymous · Answer

Carter wants to know if warming up will help runners sprint faster. Thirty track and field athletes volunteered to participate in his study. He randomly assigns 15 athletes to warm-up for 10 minutes. All 30 participants sprint the same distance. He calculates the mean for each group and determines that the mean for the warm-up group was 10.7 seconds and the mean for the other group was 13.2 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 Carter conclude from his study?

anonymous · Answer

attachment

anonymous · Answer

The difference in the means is significant because a difference of 2.5 is very likely.
The difference in the means is not significant because a difference of 2.5 is very likely.
The difference in the means is significant because a difference of 2.5 is not very likely.
The difference in the means is not significant because a difference of 2.5 is not very likely.

jim_thompson5910 · Answer

+2.5 is not on the dot plot but -2.5 is

so let's focus on that

jim_thompson5910 · Answer

how many dots are over the -2.5 ?

how many dots are there total?

anonymous · Answer

Okay, thought of that too.

anonymous · Answer

-2.5:  4
Total:  30

jim_thompson5910 · Answer

I count 3 over -2.5
there are more than 30 points/dots total

jim_thompson5910 · Answer

try again

anonymous · Answer

Oh sorry! My vision is a bit blurred.

anonymous · Answer

Okay so there are three dots over at -2.5, as for total there are 54.

jim_thompson5910 · Answer

yep

anonymous · Answer

....I'm so sorry my vision is really messed up right now.

jim_thompson5910 · Answer

that's ok

jim_thompson5910 · Answer

so if you randomly picked out a dot, where are you most likely to land?

anonymous · Answer

-1.0?

anonymous · Answer

You there?

jim_thompson5910 · Answer

yes, so what this means is that it's not likely to get -2.5 or +2.5

telling us that a difference of 2.5 is not very likely (positive or negative)

he got a difference of -2.5 (10.7 - 13.2 = -2.5) 

So the difference is significant because his null hypothesis is rejected

jim_thompson5910 · Answer

In short, the answer is "The difference in the means is significant because a difference of 2.5 is not very likely."

anonymous · Answer

Okay! That makes sense and it was easy.  Could you help me with one more, please?

jim_thompson5910 · Answer

ok

jim_thompson5910 · Answer

I'll be right back but will answer the question when I get back

jim_thompson5910 · Answer

ok I'm back