Chapter 1. Matched Pairs t Procedures

true
Stat Tutor
true
true

1:11

Question 1.1

ppyHZfI4p/Yso13vvBjcg20lQ7bvnAVlfA3iX/ue9HHITd3Xa2OoIPQzjsie53PDuQOwiStHOPqsMXwX2KZS0NkXK8fi2iDDFcVQz9NfpYmL3OS+pHIB3WmyXnrSk78jNnkvGibbYy8cbEXSpmeAJdgMIDHopwNJar2jgMcagFc=
Correct. Analyzing matched pairs data is the most common use of a one-sample t test.
Incorrect. Analyzing matched pairs data is the most common use of a one-sample t test.
2
Try again.

1:58

Question 1.2

OijNLs4WnXXpdeyp7UhW7MV7lXoSenReRd8xMCN/I/v07s6ObgnKuvCGcEqP7RuHz3P8HU+YKo9BqkgEnWpVp3hPslE+3ybpp8JDOlY9M/tIPKWZ+/h3Oe+v0W0QEsVJmMNMlK6CZIMb41eZRTu9MaGEN+50Pk+SXddU338vfx7Q7EoGNLYLBLOJkxQc0SdF0whByZxCbIBkLhEwNyPYxgKHw/NbDNUJwQ6+y0TWI7L02U+mRuWav745NNN7VKZ/AoKlxXK2C8dH1YIXTjpBOYTssg95rRww2AoXwSV4R+ZRk0MkSoN6sU3EZbc3sXDPPldsfyYbCwbEhySbMxhw3z2vb1UKPghT6tmbMFoBGZBDCL/kUt95InRMR2SilfMHzUED5JCcHtckcr7IsXRkTHBryNXW5jfVmyljKVTD0YqcmHHoG266AOcxrwuDnaeVsYLI0O0PwoJsrGgrZjSVFTMwaJ8=
Correct. When individuals are paired in an experiment, they need to be randomly allocated to the two treatments.
Incorrect. When individuals are paired in an experiment, they need to be randomly allocated to the two treatments.
2
Try again.

2:35

Question 1.3

EXEE6w1XaIFc4Qt+/AWGMSrm7fuR1jmnMXr07c+g4yG/pRihtEeCb7jhasz1kYwzbfleZ/wblxXSDAWexKzBXV/NzEwvyjriM9O1pw92W6OreTzQVEwDoC/pGh3UKdWfFjUhonc4cm5pXF7uAQ96i4VOPCAXkp1ynmZQLyFbWlbHChFdSuIBZskuycpekeEvA0DPHiDByHrce4vbokxzPGDYDAwtJzxeog3yKXcBE+r9me9K
Correct. For each pair, we compute the difference between their two measurements.
Incorrect. For each pair, we compute the difference between their two measurements.
2
Try again.

2:54

Question 1.4

Correct. This is a true statement.
Incorrect. This is a true statement.
2
Try again.

3:33

Question 1.5

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
Correct. When two measurements are taken on each individual in an experiment, the order in which the treatments are applied needs to be randomized.
Incorrect. When two measurements are taken on each individual in an experiment, the order in which the treatments are applied needs to be randomized.
2
Try again.

3:48

Question 1.6

Correct. The one sample of differences from a matched pairs study is analyzed with a one-sample t procedure.
Incorrect. The one sample of differences from a matched pairs study is analyzed with a one-sample t procedure.
2
Try again.

Question 1.7

+VMN4Q8L/1RfJQVvkSK11i4GRTYvuiQQIS+BA2sgllLZA0wIoy0ZbUExsjami5lHWuPS395WaL4pNKaVATfhgCjfk2CtLUDJ
Correct. A difference can be positive, negative or zero.
Incorrect. A difference can be positive, negative or zero.
2
Try again.

4:57

Question 1.8

Correct. When pre- and post- treatment measurements are taken on each individual, the individuals need to be randomly selected for the study.
Incorrect. When pre- and post- treatment measurements are taken on each individual, the individuals need to be randomly selected for the study.
2
Try again.

8:07

Question 1.9

Gbbv21H6I79L1vylTBvqVZsxL86HW1Qq8C6pMJTr260RfJRUfXTuJfW4Kpk+LeTGtWW5sPWYt+LyNbD4LR250WCt23nkNAzPY7BCl1gmjY/jaEe7dv2dXxk85JEN+iMrq40F75xZSEZSCULyyDEoPma7xBiqqQhvFbPOoVCPHIFePUP6Pp00oi5+HY8Ie84FchEGyukfl64=
Correct. No difference equates to a difference of zero.
Incorrect. No difference equates to a difference of zero.
2
Try again.

9:29

Question 1.10

Correct. We analyze the differences for each pair when we analyze data for a matched pairs study. This includes plotting the differences and examining the plot for outliers.
Incorrect. We analyze the differences for each pair when we analyze data for a matched pairs study. This includes plotting the differences and examining the plot for outliers.
2
Try again.

10:44

Question 1.11

ITv8E2M7EJleq8LwH8oV3W4hIj0I+1x0J/ifKRxB48vlDJTTS+g0TAchvlIcC2zjz/fiBp+o/gV+HVriV4uIQWkQrVctY0HQYlhFHYI1saUD6HUXxaqExAyhOrbQxCKoRJH0GNYZha0vr8oUMRXWkZvIcAfJwDsuwPr7kC5jwxfYqTPgibpIMGJ2i4SUkqAu7NFZTo12RfSz7D8nr43SgIWwn6Q36+zEbgnh2J/T9YFSqEyAhOvbCHhxqNABMMN6H+Q4TFj0I1J0fgFqRGsZ1J8iUWQ=
Correct. If there is no difference, then the mean of the differences should be zero.
Incorrect. If there is no difference, then the mean of the differences should be zero.
2
Try again.

11:54

Question 1.12

JnvgTqRiYzarxmbd9DfYzR/VKmOB2FrasZueM8ODZ1PpLNrCqft5P3tUtWMHEFi910WHHMGSkFk1YOUXrzAWXC64gjYpIhwIYRxGDP+1ncyXDTN8VcKd6kEFTbdbnpiFwokAbvJxblnvVBWCZITMXLvQKoiXsR/GA2ehKvoJa0IUVEG1xkdTxmEPOlOGBZuyx3UA4VFku9LpbLeXM/hkAhsMTMIL7EmPGN+IzKlZaTp3Gub/z8dkSk2wPIH2C7S8pQoMavpPl7w31a21Q4cYkGNJ9hZxtbdeDBmfhBm9T1rxGTtlYd7e5B4ksbzbEsHqVVi+Eox1MnjT+tnnUnGTnu7hEeyfEwYPIj18JiN5KqdErXZ44J6nkPo26Pm9b31j17tTUQEp8VPbAkpFdd+zAQcXvvKX036blC/Wlu+XTvPwJ290kBuZRbOGNqLe6Gd1xgO6lI9fvYheyqczSwrUZaOQR4qY/qdoITsrMD6sd/8=
Correct. If sweetness decreased, then fresh sweetness will be larger than stored sweetness and the mean difference will be greater than zero or Ha: µd > 0.
Incorrect. If sweetness decreased, then fresh sweetness will be larger than stored sweetness and the mean difference will be greater than zero or Ha: µd > 0.
2
Try again.

12:30

Question 1.13

IpkuzVBMveJ/x4r6lMhfUxi0Ogo+GpEaNtjngnX1d6qxNriK1L3/dxtT6jsYa+9FSgYGuM3fISPmFdZN8FzfUsARcx0DxPw6gFSBTIDwTqYPOuB2KqH5PbK13D+7xbqO7fpBuozdzrOWCEiu2rnDmOsF3nWK8LOhx+zb3udNJyhFbNJ4Rj98itZzSHusqYlesCXFCmlK4GzSYfA39u7q7zLzc9m9hMwGVRcW40U+R+Id47QOUzBjGkwoizygSXrG2MzsKqo8cNu1PXnkrgtgUw==
Correct. µd represents the mean difference. Sweetness is measured and the difference equals fresh minus stored. So µd represents the mean difference in sweetness (fresh minus stored).
Incorrect. µd represents the mean difference. Sweetness is measured and the difference equals fresh minus stored. So µd represents the mean difference in sweetness (fresh minus stored).
2
Try again.

13:13

Question 1.14

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
Correct. Because the bottles are paired by belonging to the same batch, they need to be randomly allocated to the two treatments of being tasted fresh or tasted after being stored.
Incorrect. Because the bottles are paired by belonging to the same batch, they need to be randomly allocated to the two treatments of being tasted fresh or tasted after being stored.
2
Try again.

13:39

Question 1.15

Correct. Differences can be positive, negative or zero. These two differences are not wrong.
Incorrect. Differences can be positive, negative or zero. These two differences are not wrong.
2
Try again.

14:03

Question 1.16

ANNHDut8tov3VQ73l+gItB/DgCFYyJ7JOqah8QIXM19r9rjo0gdauxKMeCCrdR5zHCq8p4KHCYk49LpKYMQus0ZagRBF/aHNNyflsSUDsjLNcKRy1Zweaq8MTXxbHl5XM8dDXJ8j34yXebi/M47d78e31d+oZjDuF4Va9jAvVNOE6osw8JSlZ0Nwq/KWerefeX0xTip5ntKVgupWq0LuYE550JB95oQ4X9hec0KEVon0Fhod1p0LI3pGLx50zsGTIax08XfPK4FRZx1vYUsxV50+/Zk5zTIB7Xin0vPSBQNMoaYMR9oOMhP2dbdb9TLD+ki+BJLhVJE+vBQbLgKJIdYsh/5p4CqaCwLIa7lt0irEDVNizDaVkI34SctS5EzELODwf3zG26PYg82VfBQ3vQM9giQLbk6pfSl/pQ==
Correct. sd = 0.909 is the standard deviation of the differences where each difference is computed as fresh sweetness minus stored sweetness.
Incorrect. sd = 0.909 is the standard deviation of the differences where each difference is computed as fresh sweetness minus stored sweetness.
2
Try again.

14:34

Question 1.17

zQZboe9YLLX2NW9agEuYOz43g1zvArIqlQsMaA1kbBayW1fT+hDC7THzgPFIFl4QjBjKPojUX/lutP7qHjXgQwBj4EmlS1smMkNdHQ==
Correct. There are no data points that cause us to say, “Oh, wow!!! That’s an outlier!"
Incorrect. There are no data points that cause us to say, “Oh, wow!!! That’s an outlier!"
2
Try again.

15:00

Question 1.18

krnlheY3/YbCo2kzvzr075PC4Yca7i4heqPgQlxVyrPpTNjxZfeAT0TPSMuh7E4X772tazdgD7tcfpjwun44gPSEq3sj9nV4ggGJdSvRU29mcqX7S1C6UZrMAZ+CqzHMJuY4B3bgg1sKcSiOjpbb51P4T6ZIX9GoTJFSye8QY9b1oGsXkYjL7Lpoa7mI2Y74Zyiv1bc8Lw+y2Cq0bNjqudwpj8M=
Correct. df = number of differences minus one = 10 – 1 = 9.
Incorrect. df = number of differences minus one = 10 – 1 = 9.
2
Try again.

15:16

Question 1.19

KbUTjmiYkqEaHl6Hfrm5SwQ7UeSaiMZ15Py5zJgPasEqaIgj66/Y7PXVALrKvQyxTytv1bZjH1LE6cvBe8aXZAZ2edJW33h1MVRoM/oWSF8qnlDfkSCfis6Hz9wz6N5NSmt/u/mVBhaXlbqTQN+tF8DYbHsURfHDFyrx5eortBE=
Correct. With “>” in Ha, the test in one-sided.
Incorrect. With “>” in Ha, the test in one-sided.
2
Try again.

Question 1.20

/wAoE834vq/AuQxKvvcjrotd6iAJ5MAM1k9jm0OUWs6uLqRHraSeJIboa4VuYJYgBrau1L3k9Vkf8zSRWxMDyU26zB9J40HpIcPZbRb14AGcGw84bKdCS/p4Ji0X7jIUoCi3gX/hVwC3l+0e
Correct. 0.10 > P-value > 0.05 is greater than α = 0.05, so we should NOT reject H0.
Incorrect. 0.10 > P-value > 0.05 is greater than α = 0.05, so we should NOT reject H0.
2
Try again.

15:35

Question 1.21

acowkC19zBUrRt06Uwe/B+Bg9Yh6ylJcyZyeGP0CtIKxmAIKX+lKKE/vJynhOSQUofmTlW7+EcRXfnkJ5AG3II16QRsFRSQFENtX20FQz24yoY+lg6G7zaPTsybH7BAiZmaASzQ0u8Kfj66lq+QCuMqibTnV3lgGT+O/hSC/Pk9BDoWCco2TuN86nT0k1NueeMhmEni9dYnq/lTgDACtsotfj48DmwfRC+SWwuLomi2Jitkvwzhojw==
Correct. Even though we failed to reject H0, we do NOT have evidence to say that H0: µd = 0 is correct. Perhaps the sample size of 10 batches is too small to detect significance and we need a larger sample size.
Incorrect. Even though we failed to reject H0, we do NOT have evidence to say that H0: µd = 0 is correct. Perhaps the sample size of 10 batches is too small to detect significance and we need a larger sample size.
2
Try again.

16:21

Question 1.22

Correct. Since two incisions were made on the back of each rat and each incision was repaired with a different treatment, this is a matched pairs study.
Incorrect. Since two incisions were made on the back of each rat and each incision was repaired with a different treatment, this is a matched pairs study.
2
Try again.

17:15

Question 1.23

uC9KDbhpeS8WU42WDxZBq2TEtXZA0G1H987OLTi+4SocJQyce8w/qdjF3Es2+e8WOXlLEGcyLWK02tItjMoj+OqAyDC7C2i9ajJSXgGMOmIMYYqJKuMp36Goe4/ZzbAsqp3qkyNKEYNGcW8Q
Correct. P-value = 0.0467 is smaller than α = 0.05, so we reject H0 and declare the results statistically significant.
Incorrect. P-value = 0.0467 is smaller than α = 0.05, so we reject H0 and declare the results statistically significant.
2
Try again.

17:54

Question 1.24

wZReLeY1wI9TlhaH8ql32zv5xfxc0satEE351Rrw6wjHY56tcELzlDZzbZRztZo5MZGihKMuEeakRsGG7lk7mw1/SE+TjU/m5xqn+XZKwxZfD7oV1Z2eHoHPNJuRkfna0Ey53rFUr8UyS5e9nG/j+9yRypMo0Gp7TcGjnllD0Mv3rGuxXnchRKVMxxR9ywH3/4FZRZLeuq8ePGkh750ohuPpu+Qi5Pv23jr1grWUoZTvi0C4Tf3po2J0ZhPBkO+kwUBOR98YQDbryege/npC1OiUMZ4uWwz7njj+9D35fZBqyMzRH66KVg==
Correct. Since the difference is positive, taped strength is greater than sutured strength.
Incorrect. Since the difference is positive, taped strength is greater than sutured strength.
2
Try again.

18:52

Question 1.25

Correct. µd is the mean difference or the mean of the population of all possible differences.
Incorrect. µd is the mean difference or the mean of the population of all possible differences.
2
Try again.

19:36

Question 1.26

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
Correct. The parameter is the mean difference in time for all right-handed students where the difference is computed as difference = time to turn counterclockwise knob minus time to turn a clockwise knob.
Incorrect. The parameter is the mean difference in time for all right-handed students where the difference is computed as difference = time to turn counterclockwise knob minus time to turn a clockwise knob.
2
Try again.

20:36

Question 1.27

qx987pVbxtIwfotKgrGBFUCZfdHrT+p5Q+ndEWXcbJ1Fs2/GiB9NRJuswLsy5TaMGpPnZ6VqeyL3nLE9LHvCg5X3QiUJ8tNx3aScgqN2BHk3CFZgHaMKHs4KvEXKlTj2a3dIfgRtLt7NKWY2BhfZzf8brZMYVpAjLfdgE+RYl84CLqqOqE/vnIHy0yNTWtylG1Tce8Sc8Tr+1bMPm6MGUE/0kVBlYrJQZUzamv5HrA1ckALXnsLqUSLvbWWW15RjkOT/L8ipznl9O36YgE9zJt1NE6hm5tBu
Correct. When analyzing matched pairs data, we always plot the differences and check for outliers in the differences.
Incorrect. When analyzing matched pairs data, we always plot the differences and check for outliers in the differences.
2
Try again.

21:32

Question 1.28

cFwChplkwAQQJ1rQiyB5vJGmGh1eM0MdbG7uOR4+miXd1QQNbdFH2MBx08v+ewZzRsAmLQiJHgbiLzE42D8ehzjzW12rqynG2ySkL4R9p44yBavIoUSFk4RM0KXfj0U+AQNrmft6JwTaw37A59Z0qJL/uW4/p7HsgoIwAXxLVlg/THNRAFEG6JVLWhiSAjWuOYF2Wu/JVcY=
Correct. Since the interval for µd, namely (3.87, 22.77), does not contain the value of zero, we can conclude that µd is not zero.
Incorrect. Since the interval for µd, namely (3.87, 22.77), does not contain the value of zero, we can conclude that µd is not zero.
2
Try again.

21:46

Question 1.29

1YygayiOGi73CtdD3ec+YX7MQZTDu5M3fg2fEDBSV+E0sHMETrRiWZ6V3+IQbGpmQamJ+Mq9aiCy11Bu5KsYUfL8trNWNBNDLG0N5HDMlN1TRCpuIOd7Tna04+Q5zQsyxvOvPswEwIRiEz7KIZmhq5tyBG59kaz3ISHuxmWATwS6o8ZwyqkQoN4hi2jro5RHJK31KvKBYL/nRwFzvnntKtYYOOxJCQ9G5ZLxwJ6XZcyToLtCIfSAY9RhCIf5kCBmv9TIWfxWHGoKIGzHuNNFzAFD02qepynwvRYHvutEdfqkjHolnO6Hbq+kqyXEa5ye801FhGjZpdOZK00aTUY7gYfE3MyFuga3RGTZUday3DHdJOnuAvIJ4TpSS9iz6PF8TH070Af0ggg9aRWmp7kc5Frz8jQ=
Correct. Since difference = time to turn a counterclockwise knob minus time to turn a clockwise knob and the entire interval is positive, the average time to turn a counterclockwise knob is greater than the average time to turn a clockwise knob.
Incorrect. Since difference = time to turn a counterclockwise knob minus time to turn a clockwise knob and the entire interval is positive, the average time to turn a counterclockwise knob is greater than the average time to turn a clockwise knob.
2
Try again.