Quiz 13 Answers

Quiz 13 You scored 100 out of 100 Question 1 Your answer is CORRECT. In a hypothesis test, if the computed P-value is less than 0.001, there is very strong evidence to fail to reject the null hypothesis. reject the null hypothesis. retest with a different sample. > question2=c(6,2,7,-3,5) > mean(question2) [1] 3.4 > sd(question2) [1] 4.037326 Question 2 Your answer is CORRECT. In a experiment on relaxation techniques, subject's brain signals were measured before and after the relaxation exercises with the following results: Assuming the population is normally distributed, is there sufficient evidence to suggest that the l 1 l 2•13 1 847 relaxation exercise slowed the brain waves? (Use a=0.05) t-: 3-Cf- - o _ (3.4)/( 4.04/(sqrt(6))) Reject the null hypothesis which states there is no change in brain waves in favor of the alternate which states the brain waves slowed after relaxation. Fail to reject the null hypothesis which states there is no change in brain waves. There is not enough information to make a conclusion. Question 3 Your answer is CORRECT. An experimenter flips a coin 100 times and gets 59 heads. Test the claim that the coin is fair against the two-sided claim that it is not fair at the level a=.01. Ho: P = .5, Ha: P -::j:. .5; z = 1.83; Fail to reject Ho at the 1% significance level. c) Ho: P = .5, Ha: P -::j:. .5; z = l.80; Reject Ho at the 1% significance level. d) • Ho: P = .5, Ha: P -::j:. .5; z = 1.80; Fail to reject Ho at the 1% significance level. e) Ho: P = .5, Ha: P > .5; z = 1.83; Fail to reject Ho at the 1% significance level. Question 4 Your answer is CORRECT. Identify the most appropriate test to use for the following situatio� sk- �I/ Quart cartons of milk should contain at least 32 ounces. iA sample of 22 cartons was taken and amount of milk in ounces was recorded. We would like to determine if there is sufficient evidence exist to conclude the mean amount of milk in cartons is less than 32 ounces? n:. 2.2. Two sample t test a) b) • One sample t test c) Matched pairs d) Two sample z test Question 5 Your answer is CORRECT. To use the two sample t procedure to perform a significance test on the difference of two means, we assume: a) The populations' standard deviation are known. Assumptions ror a t\vo•sample t- test (these are used when the population standard deviations (or variance) are unknown) ate: L We ha..,e two independent SRS� from rwo distinct populations and \\i'e nleasure the same � • The samples from each population are independent. c) The distributions are exactly normal in each population. d) The sample sizes are large. variable for both .samples. 2. Both populations are normally distributed with unknown means and standard deviations. Or if each given sample size It's at least 30. Or we11 assume nomlallty. Question 6 Your answer is CORRECT. Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results: 2/6 5/13/2015 Print Test We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic? (assume the population data is normally distributed) a) t = 23.264 • t = 34.548 c) z = 34.548 d) z = 34.048 e) t = 34.048 > stick=c(26 3 ,25.3,26.1,25.6,26. 7 ,25 9) > liquid=c(16 9, 16.6, 16.5, 17 .4,17 .4,172) > mean(stick) [1] 25.98333 > sd(stick) [1] 0.4996666 > mean(liquid) [1l 17 > sd(liquid) [1] 0.394968 4 Question 7 Your answer is CORRECT. It has been observed that some persons who suffer renal failure, again suffer renal failure within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There o in the 1+,.-..�o and this group will be administered the new drug. There are 45 people are in the econd m:ou:g and this group will be administered a placebo. After one year, 1 0 of the • group has a second episode and 9% of the seco a g OUQ as a second episode. Conduct a hypothesis test to determine, at the significance level 0J)5, whether there is reason to believe that the true percentage of those in the first groug M'ho suffer a second episode is less tlian the true percentage of those in the sec_or _ u group who suffer a second episode? Select the [Alternative Hypothesis, Value of the Test Statistic]. "•: 1-s � a.. : 1'S 0( -=. 0. 0 � a) • [Pl < P2, 0.3497] b) [Pl -::j:.P2, 0.3497] c) [Pl > P2 , 0.3497] d) [Pl = P2 , 0.3497] e) [PI -::j:.P2 , 0.4497] t) None of the above Ho: P, = Pi.. HA ! ,. ' f'&. ---.;.. + (-01)(..411) .... s Question 8 Your answer is CORRECT. It has been observed that some persons who suffer colitis, again suffer colitis within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug 3/6 5/13/2015 Print Test designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups ofpeople suffering a first episode are selected. There are people in the st oug and this group will be administered the new drug. There are 75 people in the ou second group and this group will be administered a placebo. After one year, % fthe has a second episode and 9% ofthe second group has a second episode. Conduct a hypothesis test to determine, at the significance level O.DI, whether there is reason to believe that the true percentage of those in the lftrst grou12 who suffer a second e iso-de is cdifferen from the true percentage of those in the second group who suffer a second episode? Select the [Rejection Region, Decision"to Reject (RHo) or Failure to Reject (FRHo)l P-.. : . oct k . p _ : _ . 10 o • a) b) @• 1 - 1-tA : [z > -2.58 and z < 2.58, RHO] ,t.:= ·DOS p• P, � f'1- [z > 2.58, FRHo] - 2. SB [z < -2.58 or z > 2.58, FRHO] i d) [z < -2.58, RHO] e) [z < -2.58 and z > 2.58, FRHO] t) None of the above fil-\ 0 --; .0 I qnorm(.005) [1]-2.575829 ·ODS ""{�:. : (. lo - . 01) "• :. �. -=- 5 s ____ �-__ '>B O.\C\I ................, _.._ � ;,�· ---. = � r1 - f.,.;l lo R,.-e.c..\- Ho - 0 r, =-P Question 9 Ho: Your answer is CORRECT. HA.: f, �f-a. i. A private and a public university are located in the same city. For the private university, HJ.JS alumni were surveyed and 6£1:7 said that they attended at least one class reunion. For the public university, sampled alumni_ claime� �ey hav� a�ended at least one class reun � Thut of. Is th ·on. = . o1.s = d-:. � .oi.!> e-rence n th· sample prnp0Ft10ns stat1sttca1ly s1gmficant? (Use a 0.05) uS 1,. qnorm(.025) [1]-1.959964 -=. � 0· -,. 95'1'1w+ -= _ 1.ois,,W"f- a) Reject the null hypothesis which states there is no difference in the proportion ofalumni that attended at least one class reunion in favor ofthe alternate which states there is a difference in the FOl; I proportions. "t'i1,�•n _\ 1 l-'1-=t- l _ li2-) to �ec.t-tlo 'I-&' (1- t.,;-°T-, 101-ft I ) lv'+ff C - l't'l - j. 141 )0 ) + --------'-/ 048' I, 11 \ -\.1 > .:...: l 'I�-:..::. --I'� ,q b) • Fail to reject the null hypothesis. There is not enough evidence to conclude that there is a difference in the proportions. L :. O. c. 5 c) There is not enough information to make a conclusion. Question 10 Your answer is CORRECT. Mars Inc. claims that they produce M&Ms with the following distributions: 33.� ,,.... 1�- ... I Brown I 30% I Red I 20% I Yellow 1 20% I ,/ e.yu.t� I Orange 11 10% 1 Green 1 10% 1 Blue 1 10% I h-1.. h- l- 416 5/13/2015 Print Test A bag ofM&Ms was randomly selected from the grocery store shelf, and the color counts were: Tota..l:: 112.. � 1 I!: Brown Orange x2 l(]I I Red II �I Yellow I }[] / oloW'f� lffi I Green II �I Blue I JD Using the goodness of fit test to determine ifthe proportion ofM&Ms is what is claimed, what is 3. the test statistic? (.olo\Uf4-d- Gx�¼-c.l) l. _ l2 S - )-'.«,) .... (u. - �a. 4)•,. ( 1..1 - 1..2. '+) i.. -.-.z. 4 i( .a..:. � 3 > 'E'x,u.,t--c.ct a.� . .., a) x2 = 4.489 ®· x2=6.289 e) X: = 12.577 X: = 9.889 X: = 1.960 t) None of the above c) d) Question 11 Your answer is CORRECT. Mars Inc. claims that they produce M&Ms with the following distributions: >2• I a.1. Ifa. I. at Brown 30% Red 20% Yellow 20% Orange 10% Green 10% Blue 10% I I I I lo.-,. I I I I lo. 1- I I I I I I ID-l A bag ofM&Ms was randomly selected from the grocery store shelf, and the color counts were: Tot....\ -=- l o 1- I� I!: x2 Brown Orange I }[] I I@ I Red II fill Yellow I@ I Green II fill Blue I JD Oh>kNccL Using the goodness of fit test (a = 0.10) to determine ifthe proportion ofM&Ms is what is claimed. Select the [p-value, Decision to Reject (RHo) or Failure to Reject (FRHo)l O. o, c., R a... l O\o5a.N&d.- Ex� '1�. s-�98' ·> - l2.� - �i.-1)� ( i.�-21.'f-) Gcr"-\-...d -5 3z.. \ + Z..\.� o. 00, .. .:i.lS :pj .;t. i,,2S2. a) [p-value = 0.318, RHO] '1.. + ( '3..\- �....)- ' t1.. -10.1\l. -+ ----+ C1w-\o-1-) 3.1 .... b) [p-value = 0.682, RHO] 0. 4"1 q.'f + lo. 1'\ :L. -,,_�: l Ab��\. CJ. "---- t '' - = 516 5/13/2015 @• Print Test [p-value = 0.318, FRHo] d) [p-value = 0.159, RHO] e) [p-value = 0.682, FRHo] t) None of the above f-..,..t""" : p LX > s. 8 g l '-) 1-pchisq(S.8816,5) [1] 0.3179108 > oc.. F� l t- �j�t Ito 616