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 Posted: Tue Nov 10, 2009 6:44 pm
Any help would be appreciated sad
These are the problems I have difficulty with
PG 481 #9
One of the students in the Introductory Statistics class claims to have tossed her coin 200 times and found only 42% heads. What do you think of this claim? Explain.
Ok, I worked this one out, and I didn't really find a problem. I think the claim is probable. But.. I think that's way too easy. Maybe there -is- something wrong with the claim?
PG 481 #23
When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that in fact 8% of the apples on the truck do not meet the desired standard. What's the probability that the shipment will be accepted anyway?
Ok... what? It wouldn't be accepted at all..
PG 505 #17
An insurance company checks police records on 582 accidents selected at random and notes that teenagers were behind the wheel in 91 of them.
A) Create a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.
B) Explain what your interval means.
C) Explain what "95% confidence" means.
D) A politician urging tighter restrictions on drivers licenses issued to teens says, "In one of every 5 auto accidents, a teenager is behind the wheel." Does your confidence interval support or reject this statement? Explain.
I always have trouble with confidence intervals ):
PG 527 #8
A survey investigating whether the proportion of high school seniors who own their own cars is higher than it was a decade ago finds a P-value of 0.017. Is it reasonable to conclude that more high schoolers have cars? Explain.
No, right? this stuff is too confusing crying
The rest I don't understand at all.
PG 527 #23
A company with a fleet of 150 cars found that the emissions systems of 7 out of the 22 they tested failed to meet pollution control guidelines. Is this strong evidence that moire than 20% of the fleet might be out of compliance? Test an appropriate hypothesis and state your conclusion. Be sure that appropriate assumptions and conditions are satisfied before you proceed.
PG 552 #13
Before lending someone money, banks must decide whether they can believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the applicant, totaling points they award for the person's income level, credit history, current debt burden, and so on. The higher the point total, the more convinced the bank is that its safe to make the loan. Any applicant with a lower point total than a certain cutoff score is denied a loan. We can think of this decision as a hypothesis test. Since the bank makes its profit from the interest collected on repaid loans, their null hypothesis is that the applicant will repay the loan and therefore should get the money. Only if the person's score falls below the minimum cutoff will the bank reject the null and deny the loan. This system is reasonably reliable, but, of course, sometimes there are mistakes.
A) When a person defaults on a loan, which type of error did the bank make?
B) Which kind of error is it when the bank misses an opportunity to make a loan to someone who would have repaid it?
C) Suppose the bank decides to lower the cutoff score from 250 points to 200. Is that analogous to choosing a higher or lower value of a for a hypothesis test? Explain.
D) What impact does this change in the cutoff value have on the chance of each type of error?
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Posted: Tue Nov 10, 2009 11:39 pm
humm... well I've never taken a statistics class but I can help you out with the 1st one. One of the students in the Introductory Statistics class claims to have tossed her coin 200 times and found only 42% heads. What do you think of this claim? Explain. ok so what you have to think about is what you expect the coin flips to be. So roughly speaking if you flip 10 coins you would expect about 5 of them to be heads. But most of the time it won't be exact... or they could be all heads or all tails. So why is our experiment with 200 coins different? The idea is simply this... the more you flip the closer you will get to actually 50%. And actually the probability of being not 50% will be very small. At this point you use the chi squared distribution to figure out how low the probability here is... it's a little hard to explain why this works. If you take the value of heads to be 1. The number of trials to be 200. And the probability to be .5 The formula is (value-(trials*prob)^2)/(trials*prob) so that comes out to (1-(200*.5)^2)/(200*.5) and you get the number 98.01. This is the part that I don't remember exactly... you have to figure out how many degrees of freedom this thing has and look it up on a table like this http://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm to determine the probability... its a probably like .001. But i can't remember what the degrees of freedom were... so let me get back to you on this.
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Posted: Wed Nov 11, 2009 1:28 am
Thankyou so much!! i really appreciate it whee
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Posted: Sun Feb 07, 2010 1:56 am
This is a little...late, since I just joined a few minutes earlier. But I guess I should post anyway, in case someone else needs help.
PG 481 #23
When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that in fact 8% of the apples on the truck do not meet the desired standard. What's the probability that the shipment will be accepted anyway?
Ok... what? It wouldn't be accepted at all..
No, even if it's 8% unacceptable, because we do not check ALL the apples, and only RANDOMLY picked 150, it is possible for the truck to be accepted.
I may need to check up on exactly how to calculate the probability, (I'm pretty sure I know it) but I don't really see the point for it now since this is the answer to something asked a long time ago.
PG 505 #17
An insurance company checks police records on 582 accidents selected at random and notes that teenagers were behind the wheel in 91 of them.
A) Create a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.
B) Explain what your interval means.
C) Explain what "95% confidence" means.
D) A politician urging tighter restrictions on drivers licenses issued to teens says, "In one of every 5 auto accidents, a teenager is behind the wheel." Does your confidence interval support or reject this statement? Explain.
I always have trouble with confidence intervals ):
Everyone has troubles with confidence intervals when they first start out, so don't worry too much. It's NOT very hard to understand it as long as you keep in mind some things (which I will state if I bother teaching this later)
Okay, to answer your question, for part A:
sample size n=582
probability of teenage drivers = p = 91/582 = 0.1564 (4s.f.)
the formula for standard error is: s.e = {[p*(1-p)]/n}^(1/2) = 0.01506 (4s.f.)
(It's not so hard once you write it down)
95% confidence interval: 0.1564 +- (it's + above the minus) 1.96*0.01506 = 0.127 to 0.186 or commonly written as (0.127, 0.186)
B) Explain what your interval means.
The 95% confidence interval means that I am 95% confident that the percentage of teenage drivers is between 0.127*100% and 0.186*100%.
C) Explain what "95% confidence" means.
95% of all intervals constructed will cover the population parameter with repeated sampling.
D) A politician urging tighter restrictions on drivers licenses issued to teens says, "In one of every 5 auto accidents, a teenager is behind the wheel." Does your confidence interval support or reject this statement? Explain.
Reject, because the confidence interval is lower than 0.2 (what the politician said).
Sorry for not answering everything, but it's tiring trying to translate all the maths by typing, and I don't really see the need to answer everything since this is asked a long time ago. If anyone want help with something stats related, pm me, and I will try to get back asap.
Thanks.
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Posted: Sun Feb 07, 2010 11:20 am
well thanks for answering what you could anyway... I didn't understand them myself... I still don't lol, but that's ok I'm not taking a stats class...
btw for the +- you can literally write out (+ or -) and I think people would understand. But I agree with you that typing it out is annoying. I've been thinking of using an online blackboard to help teach the problem.. but for that we need both parties to be online at the same time... which is annoying >>. Or you can just save a picture of you solving the problem and put the picture here.
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Posted: Fri Jul 12, 2013 3:06 am
That's a good option you going for as Statistics requires class,their are many of the concepts you wont get until someone teaches you personally.
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