Question

One of the dumbest questions ever to grace an algebra II test... help appreciated.

Sugary Cookie Company has two different manufacturing plants. Company officials want to test whether each plant fills the bags with the same number of ounces. A random sample of cookie bags from plant A had a mean of 24.7 ounces in each bag. A random sample from plant B had a mean of 23.2 ounces. They randomized the data over 100 trials and the difference of means for each trial is shown in the dot plot below. What can Sugary Cookie Company conclude from this study?

Answer 1

There is a table of values where the values are ordered as
X , Y
-2.5 = 3 ***
-2.0 = 5 *****
-1.5 = 8 ********
-1.0 = 12 ************
0.0 = 9 *********
0.5 = 8 ********
1.0 = 5 *****
1.5 = 1 *
2.0 = 0
2.5 = 5 *****

1) The difference is significant because a difference of 1.5 is not very likely.
2) The difference is significant because a difference of 1.5 is very likely.
3) The difference is not significant because a difference of 1.5 is very likely.
4) The difference is not significant because a difference of 1.5 is not very likely.

Answer 2

I got tricked by this once before in a pretest.. where it asked about the difference of 1.0 ounces (instead of 1.5) (same values in table) and claimed that a score of 5 was a 'very likely' event, and therefore not significant. I didn't consider 5% a very likely event, if you were looking to be the same, so I got it wrong.

Now @ 1.5 and a score of 1, I wonder statistically what is a very likely event? Is 1:100 considered very likely? In the universe this would seem like a very sure thing, but in a gambling table that's a long shot.

And what is the measure of 'significant' ? Is 'significance' some kind of mathematical concept that I'm missing? Or is it just some measure of a standard that we are to assume the company is using? Where significant would mean it is outside of the standards set by the company.

Clearly the bags weights are all over the place, but falling roughly within +/- 3ounces. Is this considered good enough for the company? And therefore not significant?

Perhaps we are supposed to recognize instead that the data falls in a bell curve that centers somewhere around 0, so the difference (of what btw. the original random sample?) is not significant.

which just leaves the question of.. is 1:100 a very likely event or not?

Answer 3

looks like a histogram that the mean and standard deviation and what not can be assessed

Answer 4

maybe a quartile test .... or percentile as the case maybe

options 1 and 3 are the only ones that make sense to me

Answer 5

thnx.. update.. for anyone else with this problem

'significance' it seems is a subjective thing, depending on whoever is doing the measurement. There is 'practical significance' and 'statistical significance'. While a difference of 3% might be statistically significant, it could mean nothing to the company, say if 100 ounces vs 103 ounces were dispensed. So they could have set this to .01 or .05 or .1

Quote From wiki under 'statistical significance' = "P-values are often coupled to a significance or alpha (α) level, which is also set ahead of time, usually at 0.05 (5%). Thus, if a p-value was found to be less than 0.05, then the result would be considered statistically significant and the null hypothesis would be rejected"

We should probably assume the standard of 5%

As the x point in question appears to be 1.5, and the value is less than 5 in 100, then we have a p value of less than 5.

therefore we are statistically significant because we are not very likely.

Answer 6

if the p value turned out to be 5 or more though, then the difference would be
not significant because it would be considered very likely.

Answer 7

That is deep :o