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1 Exercises Right versus left The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking 25 right-handed students to turn a knob (with their right hands) that moved an indicator. There were two identical instruments, one with a right-hand thread (the knob turns clockwise) and the other with a left-hand thread (the knob must be turned counterclockwise). Each of the 25 students used both • instruments in a random order. The following table gives the times in seconds each subject took to move the indicator a fixed distance:30 e Subject RignTthread Leffthread 1 . 113 137 2 105 3 130 133 /I y 4 101 108 l| 5 138 115 ;] 6 118 • 87 103 8 116 145 9 75 78 10 96 107 84 / 13 116 / I 14 107 87 15 118 1R" 123 1-8- -W4 135 19 111 88 78 101 123 J:T»S x*^ Po«-r^r ru ^-o-c^ A /WjV ^° 1 148 147 103 25 /rbSIG*J I 103 111 23 24 100 89 85 76 116 5o THAT LJ e £7=FecT ft i/c M r *n"^^ Lol-VttH /4vjf2.AC£. OuT -k t>A/Alcy THe" l</^0^ 15 1 ' 122 16 93 (a) Explain why it was important to randomly assign the order in which each subject used the two knobs. 1? 11 17 Left thread 89 78 . 22 i* 12 146 Right thread 20 21 |—' 105 7 Subject " O"5fcD fl y^a^r^. \O I\U t -»0^TTV5 / 'r / ^ ^^ r' ^N f 5^5 ^5 ^***^ . -^ ^ . - _ o/'T'Tesr r> It m _. fN ^^Lo — ^^ £_ >A-° r *., ^ ———-~—__^_A_ ^>o »*^ f \ c= ^-VcV ^ ss / 3 3 T_ CO 00 '*• 1* (£ *j e T /tit*. ci,'<L A^^-f-trrT, (b) The project designers hoped to show thatrigKFn handed people find right-hand threads easier to use. Carry out a significance test at the 5% significance level to investigate this claim. J ^pU^. , -Q ^A * ~tf^ T^b i= -o?«l ^^ ? - . 0037 ±<o 14 * / ^~i- •* A • ^d "r ° **-j * H ^ ~ * - ,00 7§ STscc ^^t^r T^i- T em pUUL ' ?> _ Lz- ,— ^«~ 9$ 94. Significance and sample size A study with 5000 subjects reported a result that was statistically significant at the 5% level. Explain why this result might ._ PO+ not be particularly large or important. . 95 Sampling shoppers A marketing consultant observes 50 consecutive shcippers at a supermarket, recording how much each shopper spends in the store Explain why it would not be wise to use these 0F U) I TH fa-Df5«c«lfo UJfLL " '. THiAi62 A Cdd i-£i Cu/sJ V f /vJI fA4 CG ° 5AM /vfc/r 3 /?c/»«/ iVfce 96. Ages of presidents Joe is writing a report on the backgrounds of American presidents. He looks up the ages of all the presidents when they entered office. Because Joe took a statistics course, he uses these numbers to perform a- significance test about the mean age of all U.S. presidents. Explain why this makes no sense. _ K o 4- 97. Do you have ESP? A researcher looking for evidence of extrasensory perception (ESP) tests 500 subjects. Four of these subjects do significantly better (P< 0.0 1) than random guessing. (a) Is it proper to conclude that these four people have ESP? Explain your answer. (b) What should the researcher now do to test whether any of these four subjects have ESP? 0\V Sola', *vo '•»• ««/.«. S /° fb , 6^ -pro c<r ck>/«_ I 5/I O«/ |7 ^< Test of Significance Template Parameter of Interest Choice of ^ s cuej°c^ met~" i^'^v: •* **—3i^ j^ ^4^- oM^ '- Vr"-* Significance ^=.,v English: ^MulJ s,>- /V- . AO ^ li . w« <5A-i»i/' §VJ,, t Hypothesis Alternative Hypothesis Symbols: LJ . .' English: -^ . Doe x . 4 Symbols: /, |4^- —O SfJ \ "K ^<e <^S J J'o^c^t?^ -te » /^.^ "> 6 \/ \ TU,i^> ( j_ ^iJ tlrvat, le + f THt^ ^^ secu^^^ Conditions of >. co>'.- ^ •<„';. t_oci<b rA\*L x / W"1^ cT*J-\<- ^-^i^ /V iBc> PLOT - Sketch of the sampling distribution of the sample statistic under the null hypothesis, indicating the mean: s' ~x \~ —' 1' ' Sampling Distribution § ^ ^.<L vtJTr-t i 1 1 ' \ J5.53. •. Formula: — . * -M tatistic ^ Plug-ins & Value: ^ Sfi 7-.r-> j _ ,„ <3-3a-c, Use correct probability notation. P-value Meaning of the P-value % '^ T^^v-U 5o u,, ,^,, ^^Reject null hypothesis O Significant result O Fail to reject null hypothesis O Not Significant result Wo English: °f" "S'^Cei cor p y c \ v / < d <T .OS' to € r^jetH" ^o - on 4 rc<w