INTR STATISTCL REASONING
INTR STATISTCL REASONING STAT 110
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This 8 page Class Notes was uploaded by Shane Marks on Monday October 26, 2015. The Class Notes belongs to STAT 110 at University of South Carolina - Columbia taught by L. Hendrix in Fall. Since its upload, it has received 48 views. For similar materials see /class/229650/stat-110-university-of-south-carolina-columbia in Statistics at University of South Carolina - Columbia.
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Date Created: 10/26/15
452010 Chapter 22 What is a Test of Significance Acompany claims that it has only a 5 complaint rate for its products A consumer protection group thinks the percent is higher Asurvey of a random sample of 400 product owners shows that 33 had complaints 1 IS a 005400 00001 d 33400 2 0083 b 00533 0001 c E z 001 400 Acompany claims that it has only a 5 complaint rate for its products A survey of a random sample of 400 product owners show that 33 had co l ints mp a lfp is really 005 the mean of 3 s sampling distribution is a 005400 00001 d 33400 2 0083 b 00533 0001 e w g 001 0 05 400 7 z 001 c 400 f 005 452010 Acompany claims that it has only a 5 complaint rate for its products A survey of a random sample of 400 product owners show that 33 had complaints lfp is really 005 the standard deviation of 3 s sampling distribution is a 005400 00001 d 33400 2 0083 b 00533 0001 e w a 001 400 o 5 7 z 001 c 400 r 005 Acompany claims that it has only a 5 complaint rate for its products lfp is really 005 the standard deviation of p for a sample of size 400 is 001 lfp is really 005 what is the probability that a f of 8 or more would be observed A 0135 D 997 B 02 E 99865 C 5 This is an example of a Hypothesis Test The claim that p005 is What is called the Null Hypothesis The probability 0135 is called the pvalue It is similarto the probability in a criminaltrial using DNA evidence a small number is evidence against the Null Hypothesis 452010 A hypothesis test checks sample data against a claim or assumption about the population The claim or assumption being tested is called the null hypothesis such as H0 p 050 The null hypothesis is the status quo It is always set up using an equal sign Fortests about a proportion the value ofthe null hypothesis is the mean of the normal distribution we will use to calculate the pvalue The statement we are looking for evidence of is called the alternative hypothesis Three possible alternate hypotheses for the above null hypothesis are 1 Ha p lt 050 or 2 Ha p gt 050 or 3 Ha p is not equal to 050 The alternative hypothesis is the experimental hypothesis It is opposed to the null hypothesis 452010 Fortests about a proportion the alternate hypothesis tells which probability should be calculated from the normal curve A new drug is advertised as being 80 effective A consumer advocacy group thinks that it isn t that effective and is looking for evidence that it doesn t work well What is the null hypothesis What is the alternate hypothesis Historically 76 of students in an introductory psychology course have correctly answered the professor s favorite test question on Freud This semester the professor gave a randomly selected group of students an extra lecture on the subject and wants to see if it will help them do better on the question The null hypothesis H0 should be A p lt 076 D p076 B p 076 E plt024 C p gt 076 452010 Historically 76 of students in an introductory psychology course have correctly answered the professor s favorite test question on Freud This semester the professor gave a randomly selected group of students an extra lecture on the subject and wants to see if it will help them do better on the question The alternate hypothesis HA should be D A p lt 076 p076 B p 076 E plt024 C p gt 076 The pvalue is used to summarize the amount of evidence we have against the null hypothesis The pvalue is the probability that we ould see a statistic at least as extreme as the one observed if the null hypothesis was true The smaller the pvalue the more evidence against the null hypothesis The Level of significance 0c determines how much evidence against H0 we require to reject H0 and find in favor ofthe alternative hypothesis Ha lfthe pvalue is less than octhen we have statistically significant evidence against the null hypothesis 452010 With a pvalue of 00436 and an on of 005 we would A Reject the null hypothesis and conclude the alternate hypothesis wastrue B Conclude that we do not have enough evidence to reject the null hypothesis a ii x my WWW a uayspasvsxemcennanspianwimccr lb 0 LBWalhasulnnlhemudlneuSuttlemlna m mull ham ugxgngaimaimggsymea AW reduction in mama aivoo wltliln an days any scr and achieved astgnmai Pvalli am 1st mlh a hazard m at has lSS Vu cannilencs Inlawal arms2 as in In mum miner aiilynsut minim in m Dravhylaxis m and we huliant m ma cuntml arm in sti ilmn At what a Ievel would you be able to reject the null hypothesis HD effectiveness0 so it didn t work using the circled pvalue A a001 B a005 C a010 If the null hypothesis was really true then the probability that you reject the null hypothesis is ual to on So you should pick on to be the chance you are willing to take of rejecting HEl when it is really true If HD is the person is did not commit murder then you probably want a small u because on ist e probability you would reject HEl and say an innocent person was guilty a005 would be very bad in this case 452010 It is important to pick on in advance before you get your pvalue Otherwise you could just pick your on later so that you could reject the null hypothesis only if you wanted to In this case drug companies could always claim that their drug worked Hmmm my pvalue was 0078 so I ll pick onto be 008 so that I can reject HD mm The null hypothesis HD is the status quo It is always set up using an equal sign The alternative hypothesis HA is the experimental hypothesis it is what we are looking for evidence of It involves either lt gt or The pvalue is the probability that we would see a statistic at least as extreme as the one observed if the null hypothesis was true It measures the amount of evidence we have against HEl smaller is more evidence Back to the example The null hypothesis HD is that there is no effect of the new drug VOD reduction0 The alternative hypothesis HA is that the new drug works VOD reduction gt 0 The pvalue of 00539 means that there is only a 539 chance we would see this much evidence against the null hypothesis see this much evidence the drugged worked if it really didn t work The question is is this a small enough probability The key points The Level of significance on determines how much evidence against H we require to reject HEl and find in favor of the alternative hypothesis Ha We reject HEl if the pvalue is S on If pvalue gt awe don t know HEl is true we just don t have enough evidence to say that it s false 452010 It s also importantto note that being statistically significant having a pvalue S a doesn t necessarily mean that your result is actually important Determining if the result is actually important is determiningthe practical signi cance of the result Defibrotide from the example is used to prevent blood clots Even if the results of the study are not statisticalysigni cant they may still be practically signi cant