Question

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 counter-clockwise). The table below gives the times required (in seconds) to move the indicator a fixed distance.

Subject ID	Right-hand Thread	Left-hand Thread
1	113	137
2	105	105
3	130	133
4	101	108
5	138	115
6	118	170
7	87	103
8	116	145
9	75	78
10	96	107
11	122	84
12	103	148
13	116	147
14	107	87
15	118	166
16	103	146
17	111	123
18	104	135
19	111	112
20	89	93
21	78	76
22	100	116
23	89	78
24	85	101
25	88	123

1. The project hoped to show that right-handed people find right-hand threads easier to use. State the appropriate H_o and H_a about the mean time required to complete the task.
2. Carry out a test of your hypotheses. Give the P-value, report and explain your conclusion in a brief paragraph.

Answer 1

Sabution Subyet Right -hand Thad Left hand d Right hand Thread -left hand Thread Thaead TD 13 24 137 os oS 30 133 -3 3 lo8 -7 lo 23 s 138 70 18 -I6 l03 87 45 AG O 78 75 -I 96 lo7 22 38 -45 03 48 31 147 3 lo7 166 48 811 5 46 lo3 43 I6 -12 135 to4 -31 11 १३ 89 T8 -16 78 23 85 01 35 88 95 Σ- -333 1

Noc to find the d a) - 333 25 d-13.32 Now to find the standand deviahion Idi-) Sd= (0+13.32)+(-3+ 13.32 ) + (=1+13.32) t1613.32)t 13.92) -61332) t (:3541332)2 (-24 t13.3) 25-1 a625.4 Sd 24 SV526.06 = a.136 Naa tostate the null and Atemativeyfothesis Null hyftesia Hto : HR-L 0 Attenative yfothesis : R-L<o two obsesvations Fteoie we will Pained t-test Sjnce here asie one Subjedt Nocs to find the test-statistic -13.32 t 22.135

-13.32 t- 22.936 5 -13.32 4.58 12 t =-2.90 Now to find the degnees of faredom- |- u =P 25- df Nos to find the PValue :- fheor using the values of degices of feedom ad test- statistic then ae get the P-vatue P-Value Decision = a0039 PValue <d 0.0039 0.05 Thenefae of sigificane e eiet the mull yfethesis (H) at 0-os fvel Condusion Thene is statistially sijnifiant eVdence tSufpit the hyathesis that Jight hande feople find ight hand treads Pasies to use