solution

 

. The design of controls and instruments has a large effect on 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 by screw action. 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 turns counterclockwise). The table below gives the times required (in seconds) to move the indicator a fixed distance:11 DATADATA

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DATA FILE

CONTROLS

$1rn $1rn $1rn $1rn $1rn $1rn$1rn Right$1rn    Left$1rn $1rn $1rn $1rn $1rn   Right$1rn$1rn Left

$1rn $1rn Subject$1rn$1rn thread$1rn   thread$1rn Subject$1rn thread$1rn  thread

$1rn $1rn    1$1rn $1rn $1rn$1rn 113$1rn $1rn    137$1rn $1rn   14$1rn $1rn   107$1rn $1rn 87

$1rn $1rn    2$1rn $1rn $1rn$1rn 105$1rn $1rn   105$1rn $1rn   15$1rn $1rn   118$1rn$1rn 166

$1rn $1rn    3$1rn $1rn $1rn$1rn 130$1rn $1rn   133$1rn $1rn   16$1rn $1rn  103$1rn$1rn 146

$1rn $1rn    4$1rn $1rn $1rn    101$1rn $1rn    108$1rn $1rn  17$1rn $1rn   111$1rn$1rn 123

$1rn $1rn    5$1rn $1rn $1rn    138$1rn $1rn    115$1rn $1rn 18$1rn $1rn$1rn 104$1rn$1rn 135

$1rn $1rn    6$1rn $1rn $1rn$1rn 118$1rn $1rn   170$1rn $1rn 19$1rn $1rn    111$1rn$1rn 112

$1rn $1rn   7$1rn $1rn $1rn $1rn 87$1rn $1rn$1rn 103$1rn $1rn 20$1rn $1rn$1rn 89$1rn $1rn  93

$1rn $1rn  8$1rn $1rn $1rn$1rn 116$1rn $1rn    145$1rn $1rn 21$1rn $1rn$1rn 78$1rn $1rn  76

$1rn $1rn  9$1rn $1rn $1rn    75$1rn $1rn $1rn 78$1rn $1rn    22$1rn $1rn$1rn 100$1rn$1rn 116

10 96 107 23 89 78

11 122 84 24 85 101

12 103 148 25 88 123

13 116 147

(a) Each of the 25 students used both instruments. Discuss briefly

how the experiment should be arranged and how randomization

should be used.

(b) The project hoped to show that right-handed people find

right-hand threads easier to use. State the appropriate H0 and

Ha about the mean time required to complete the task.

(c) Carry out a test of your hypotheses. Give the P-value and

report your conclusions.