Question

i just need someone to check and see if these Probability and Statistics questions are right .....
A. Jose spins the spinner 8 times. In those 8 spins, the arrow never lands on 3. Based on this information, is the spinner unfair? Explain.
Well there only one number 3 so that will be (1/4) that equals 25% the spinner together equals 100% so if the spinner is spin 8 times and doesn't land on a 3 he should be concerned.

Answer 1

B. Jose spins the spinner 500 times. In those 500 spins, the arrow lands on 3 a total of 42 times. Based on this information, should Jose be concerned that the spinner is unfair? Explain.Yes the spinner is begin unfair again he has a 25% chance to get the 3 if you multiply 25% by 500 you get 125 if you divide 125 by 500 it equals 25% again so if 42/500 equals 8.4% you know something has to be wrong

Answer 2

I think those are smart answers but dividing into 4 still doesnt make a differ. It depends on how he used it but still good answers and on b i would say about 100 or atleast 75 for the 3 so your doing this right and smart

Answer 3

Your being reasonable

Answer 4

so it could be a right answer?

Answer 5

A) think about your answer, if you flip a coin twice does that guarantee exactly one heads and one tails? Of course not.
To find the probability of not landing on a 3 8 times in a row, take the probability of not landing on a 3 in one spin and take the 8th power (multiply it by itself 8 times)
So the chance of not landing on a 3 8 times in a row is (.75)^8 = .10 = 10%, so you should NOT be concerned.

Answer 6

Yes @garcia101

Answer 7

Your answer to part B is correct, though.

Answer 8

I think they are right cause basicaly this is ur opinion and the statistics so when you put them together it is resonable like here and your answer really sounds liek the best explanation I ever encountered

Answer 9

A is right too I belive

Answer 10

Statistics is NOT based on opinion, it's a based on generalized assumptions of the most reasonable occurrences based on chance. There's a 10% chance of not landing on a 3 after 8 spins, not a 100% chance. Whether that 10% chance is significant enough to be concerned about is the part of statistics that is open to interpretation. Usually 10% is a large enough chance with a small number of trials(8) that there should be no reason to be concerned.

Answer 11

But he should of said, since it was spinned 8 times, atleast once it should have landed on three, otherwise it unfair and she should be concerned on why its not landing, meaning the probability and its location can interfere

Answer 12

but anyways gtg

Answer 13

and @dagrothus I didnt say the opinion is based on statistics I said he had to use his opinion and statiscs tomake a reasonable answer, -_-

Answer 14

Meaning this has to make sense along with what you think it should be adressed to.

Answer 15

Also, remember that variance for the binomial distribution is npq, so in 8 spins, with p=0.25 and q=0.75 than var=1.5 or standard deviation is 1.22.

So you would expect that with 8 spins, the number of times that it comes up "3" is \(0.25*8 \pm 1.22\) or between 0.78 and 3.22 times. So coming up zero times is not much less than 0.78 for part A.

Answer 16

Use the same idea for part B

Answer 17

@ybarrap im sorry i dont understand can you please explain

Answer 18

this is the spinner being used

Answer 19

For 500, npq=18.75. So "3" should come up about \(500*0.25 \pm 4.3\) or between 129.7 and 129.3, which is where about 68% of your samples should be (based on the central limit theorem).

The more samples you have, the more the average will come closer to the sample average will get to the expected value of 0.25*500 = 142. However, npq also means that variance will increase with more samples, just mainly do to the fact that if you have more samples, you'll have more dispersion.

Given these results, 42 seems very low compared to the expected lower bound of 129.7.

Answer 20

Here is some info on the binomial distribution - http://en.wikipedia.org/wiki/Binomial_distribution
Central Limit Theorem -
http://en.wikipedia.org/wiki/Central_limit_theorem

Answer 21

@ybarrap my class hasnt learn binomial distribution yet this is unit 3 we wont learn that until unit 4

Answer 22

@garcia101 since they are asking you intuition-type questions and will be followed by a more quantitative approach, I think that you're reasoning for both is well-founded. However, in case A, I would think that 0 is not much different from, 2, the expected number of outcomes; so I could conclude one way or the other that the spinner was bias with such a low number of samples.

Answer 23

@ybarrap in other words the answer is wrong???

Answer 24

25% times 8 = 2 and 2 times 4 =8 so if the spinner doesn't land on 8 then he shouldn't worry about it

Answer 25

It's not wrong, because even using standard statistical testing there will be some cases where even a biased spinner will be in range. The point of this subjective exercise to to gain an intuitive feel for likelihood of an observed outcome. The result should be that without the right tools (i.e. statistics), it's difficult to justify any answer. However, given what you do know, the expected value of 2 for case A but getting 0 should not be too surprising given the low number of samples (i.e. 8). In other words, I would not be confident in saying the spinner is biased.

In case B, the point there is that even without the right statistical toolset, getting 42 rather than something in the range of 125 seems very unlikely for a spinner that is unbiased. So in this case, I would lean heavily in the direction, given this new evidence (i.e. many more samples), that this spinner IS biased.

That should be the primary take-away for these two problems.

Answer 26

so???

Answer 27

Not sure what more can be said. Answer is Accept that is unbiased or reject the hypothesis that spinner is unbiased

A. Here we say here that we can not reject the hypothesis that the spinner is unbiased mainly due to the low number of samples. So we accept the hypothesis that the spinner is unbiased.

B. It is unlikely to get a result like 42 if the spinner were not biased. Here we would reject the hypothesis that the spinner is unbiased and accept the alternative, that the spinner IS biased.

\(\underline {Summary}\)

A. Unbiased
B. Biased

Answer 28

so those are the answer the ones i wrote arent???

Answer 29

@ybarrap???

Answer 30

For A it seems you thought is was "unfair" and for B it seemed like you also said "unfair"

For A I said "fair" and B "unfair" for the reasons above.

Answer 31

ok