STATISTICAL METHODS STAT 302
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This 5 page Class Notes was uploaded by Celestino Bergnaum on Wednesday October 21, 2015. The Class Notes belongs to STAT 302 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 28 views. For similar materials see /class/225757/stat-302-texas-a-m-university in Statistics at Texas A&M University.
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Date Created: 10/21/15
Sample Test Questions 1 As we keep tossing a coin as 11 increases which of the following happens A The sample proportion 17 gets smaller B The sample proportion 17 gets closer to TE the population proportion C The standard deviation of the sample proportion op gets smaller D All of the above will happen E Only two of the above will happen 2 Why use or report an average of several observations instead of just one A You could have made a mistake with one but it s less likely you d make the same mistake with several B The average is less biased than any individual observation C An average can t be an outlier D Averages are less variable than the individual observations E An individual observation can t represent the mean of a whole population 90 lLower Limit 10177573 lUpper Limit 11822427 95 lLower Limit 10020018 lUpper Limit 11979982 99 lLower Limit 97120853 lUpper Limit 12287915 3 We haven t done this exactly in class but using the chart at the bottom of the review sheet what is the correct range of the pvalue for testing H0 1 10 vs HA 1 i 10 Apvalue gt 010 B 010 gtpvalue gt 005 C 005 gtpvalue gt 001 Dpvaluelt 001 4 Which of the following is FALSE A IfI reject at the 5 level I will always reject at the 10 level B A test of hypotheses can never prove the null to be true C Assuming the data is normal and we are given the population standard deviation we use a t test if the sample size is small D A random sample is always necessary E All of the above statements are true none are false 5 What is the 79th percentile for the standard normal Z N N0 12 A 079 B 07852 C 02148 D 081 E 081 6 Let X N25 42 What is P20 lt X lt 26 A 04931 B 07043 C 04013 D 08413 E 06853 7 Suppose the standard deviation of some population 0 is 36 How large of a sample would you need for the standard deviation of the mean TX to be half as large A2 B4 C6 D9 E18 8 Let T 9 N N522 What is the range of the middle 90 of these X 9 s In other words what are fa andfb such that P E lt f 9 lt fb 090 centered at the mean 1 5 A 171 829 B 1645 1645 C 829 829 D 128 128 E 244 756 9 If I had asked for the middle 95 instead which of the following would be true A The interval would be wider since the standard deviation would be larger B The interval would be narrower since the standard deviation would be smaller C The interval would be wider since it covers more of the possible observations D The interval would be narrower since it s more accurate E The interval would be the same since the mean u and standard deviation 0 would not change 10 When is a sample size of 30 not enough to say the distribution of approximately normal A when the data is categorical and the true proportion of successes TE is less than 15 B when the data is already normal C when the data is highly skewed D All of the above are true statements E Exactly two of the above are true statements 11 Let p42 N07 00712 What is P9742 lt 05 A 05 B 0 C 09976 D 00024 E 02 12 Why do we call the distribution of the sample mean X n a sampling distribution A because it s the distribution of the sample of random observations B because we must take a sample just to get one random observation C because we sample from the distribution to nd the sample mean D because the distribution is only of a sample not the whole population E because we can t get the distribution of the whole population of sample means only samples 13 Letpza N N04 012 What is the maXimum sample proportion some 17 you most likely would observe De ne a rare event one that most likely won t happen as something with a probability of 0001 or less In other words what is 17 such that P0724 gtp 0001 A 0308 B 07 C 0708 D 043 E 04308 14 Is it reasonable to think you could get a sample proportion of 25 or less How likely is this occurrence Use the same distribution as above A 05596 B 04404 C 025 D 015 E 00668 15 While he was a prisoner of the Germans during WWII John Kerrich tossed a coin 10000 times He got 5067 heads If we say that these tosses represent a simple random sample from the population of all possible tosses of his coin is there reason to believe that his coin was biased gave too many heads to be fair Well how likely is it to get at least this proportion of heads from a fair coin NOTE The true proportion of heads for a fair coin is TE 05 and the standard deviation for this many tosses is op quot72390 7239 n 0005 A 05 it ll happen half of the time B 009 not very likely but plausible C 034 fairly likely so it s believable D 0067 rare but it could happen E 0005 pretty rare it most likely isn t a fair coin 16 Why is the Central Limit Theorem so important in the study of statistics A It allows us to use the normal distribution for any kind of data B It tells us that any data can be approximately normal if we take a large enough sample C It tells us that any sample mean can be approximately normal D It tells us that any sample mean will be unbiased E None of the above are true statements of the CLT 17 Let X N N10 32 What is PX gt18 A 09962 B 09971 C 267 D 00038 E 00029 18 Had we taken a sample of size n 25 from the population above what would the probability have been for X 9 2539 A More than for X since more X25 s are closer to the mean u B Less than for X since less X25 s would be that far from the mean u C Less than for X since less X25 s are above the mean u D The same as for X since the mean 1 is the same for both E You can t say without calculating the probability 19 Ok let s say you just got a job as a lab tech and you re going to be doing different tests on possible new drugs that your company is creating Of course the reason you got the job is because they know you have an excellent knowledge of how statistics works and they re sure you will do the job right You need to nd statistical evidence that your company s new wonder drug actually works better than Brand X which is the best selling product on the market today Now Brand X claims their effectiveness rating is 8 out of a possible 10 You however are skeptical that this is true and decide to test their product along with yours Let s call yours Brand A and let MA be your product s true mean effectiveness rating uX be the true mean effectiveness rating for Brand X First of all what hypotheses should you test A Ho MA MK vs HA HA i Hx 13 H05 HA HX VS HA HA lt HX C Ho MA MK vs HA MA gt Hx D HO HA 10 vs HA MA gt 8 E HO HA 8vs HA MA gt 8 20 Same scenario How are you going to go about getting the data to test your hypotheses A Take random samples of both drugs and give them to the rst 50 people who have a headache B Take two random samples of people with headaches and give one group Brand A and the other Brand X C Take one random samples of people with headaches and give every other one Brand A and the rest Brand X D Take two random samples of people with headaches and give each person one tablet of each Brand E Take a couple of aspirin yourself because all of these people are giving you a headache 21 Same scenario still Let s say you decide to test HO HA ux vs HA HA lt ux since you ve decided to use time until the headache is gone ie you re testing which drug works faster Knowing what you do about Type I and Type II errors what DtlCVCl should you use in your test Pick the answer that is most correct A Use on 010 because you want to reject as much as possible B Use on 001 because you want to reject as much as possible C Use on 010 because you don t want to claim there is insuf cient evidence when your brand is really faster D Use on 001 because you don t want to claim there is insuf cient evidence when your brand is really faster E Use on 010 because you don t want to claim your brand is better if it really isn t any faster 22 Ok your output from your test of hypotheses gives you a pvalue 0018 What can you conclude A At the 5 and 10 levels you conclude your brand gets rid of headaches faster B At the 1 level you conclude your brand gets rid of headaches faster C At the 1 level you conclude your brand takes longer to get rid of headaches D Both A and C are correct conclusions E None of the above are correct conclusions 23 Now the guy in the of ce neXt door is jealous of all the attention you ve been getting so he decides to run his own little eXperiment He takes 10 samples and calculates 90 con dence intervals for the true mean time it takes for Brand A to stop a headache From these 10 con dence intervals he nds 3 of them don t contain the mean of Brand X 15 their supposed true mean time He thinks this is substantial proof than Brand A is better What s really going on A He s correct Brand A is obviously better B He s obviously miscalculated since all 10 intervals should contain 15 C He s obviously miscalculated since all 10 intervals should NOT contain 15 D He didn t take random samples so his results are skewed E He merely had approximately 10 of the intervals not contain the true mean 15 24 So we re still worried about this jealous guy Now he s doing a hypothesis test You KNOW that there s is no evidence that Brand A is better than Brand X You ve tested it a zillion times Obviously to you your company s product is only just as good But the boss really wants to say it s better and the guy next door wants to make him happy Which of following would lead them the boss and your neighbor to the wrong conclusion but the one they want Remember the null is that the brands are the same the alternative is that Brand A is better A a Type I error B a Type II error C a test with a very small DtlCVCl D switching the null and alternative hypotheses E It is impossible to claim Brand A is better because it really is only just as good 25 If con dence intervals can tell us the same thing that a hypothesis test can why would we ever need to run hypothesis tests anyway A There s no reason it s just a different way to do analyze data B Hypothesis tests are more accurate because you are testing an exact value fori or 7 C Hypothesis tests can test two samples but con dence intervals are only for one sample D Hypothesis tests can have smaller pvalues since you can run one sided tests gt or lt but con dence intervals are only equivalent to two sided tests E Exactly two of the above are true 26 Which of the following BEST describes what 95 con dence means in a 95 con dence interval for p of 7894 A There is a 95 probability that p is between 78 and 94 B In repeated sampling 1 will fall between 78 and 94 about 95 of the time C In repeated sampling about 95 of the observations will fall between 78 and 94 D In repeated sampling about 95 of the observations will fall within the con dence interval E In repeated sampling the con dence intervals will contain 1 about 95 of the time H01I 05 vs HA n lt 05p 04 and pvalue 0079 27 Looking at the graph above what would have happened if we had gotten a sample proportion 17 030 instead A The conclusion would have been exactly the same B The value of the test statistic would have increased C The value of the pvalue would have decreased D The value of the pvalue would have increased E The probability of making a Type I error would have decreased H0 1 12 vs HA 1 gt12 f15 and pvalue 0029 28 Which of the following is the best de nition of the pvalue in terms of the test represented above A The pvalue 0029 says that 971 of the time we will get sample means of 15 or more when the true mean is only 12 B The pvalue 0029 says that 971 of the time we will get sample means of 12 or more when the true mean is only 15 C The pvalue 0029 says that there is a 29 chance that the true mean is only 15 D The pvalue 0029 says that there is a 29 chance that the true mean is greater than 12 E The pvalue 0029 says that 29 of the time we will get sample means of 15 or more when the true mean is only 12 29 Which of the following de nes the signi cance level of a hypothesis test 0 A how often we make a Type I error B how often we reject H0 C how often H0 is false D how often H0 is true E Exactly two of the above excluding D 30 Z N N0 12 What is 2 such that P7z lt Z lt 2 025 A i0675 B 0625 C 05987 D i115 E i032
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