Question

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 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). Each of the 25 students used both instruments. The table gives the times in seconds each subject took to move the indicator a fixed distance.

Performance time (seconds) using right‑hand and left‑hand threads

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

1) Each of the 25 students used both instruments. Select the correct explanation describing how randomization works in arranging the experiment.

a) For each subject, randomly select which knob (right or left) that subject should use first.

b) For each knob, randomly select which student will turn it

c) For each instrument, randomly select which student should use it.

d) For each subject, randomly select which hand that subject should use first.

2) The project hoped to show that right‑handed people find right‑hand threads easier to use. Let μ be the mean difference in the time needed to do the action (right minus left). State the hypotheses you should use to reach a conclusion.

a) H0:μ=0

b) Ha:μ<0

c) H0:μ≤0

d) Ha:μ>0

e) H0:μ=0

f) Ha:μ≠0

g) H0:μ=0

h) Ha:μ>0

Make a stemplot from the data, then select the correct stemplot from the options.

3
2	1 5
1	0 1 3 8
0	0 1 3 3 4 7
−0	6 6 6 2 1
−1	9 4 1 1
−2	5 5 3
−3	8 2
−4
−5
−6

3	8
2	0 3
1	1
0	2
−0	7 4 3 3 1 0
−1	6 6 6 2 1
−2	9 4
−3	5 1 1
−4	8 5 3
−5	2
−6

3	0 1 1 3 3 3 7 8
2	0 1 1 4
1	6 6 6
0	1 1 4 5 5 9
−0
−1	2 1
−2
−3	3
−4	8 2
−5
−6

3	8
2	0 3
1	1
0	2
−0	2
−1	2 1
−2	4
−3	6 6 6 5 1 1
−4	9 8 5 4 3
−5	7 4 3 3 1 0
−6

Calculate the mean x¯ and standard deviation, s. (Enter your answer rounded to three decimal places.)

x¯=

s=

Calculate the t‑statistic. (Enter your answer rounded to two decimal places.)

t=

Find the degrees of freedom, df . (Enter your answer as a whole number.)

df=

What is the P‑value. (Enter your answer rounded to four decimal places.)

P=

CONCLUDE: What is your conclusion?

a) Right‑handed people find right‑hand threads easier to use (P<0.01).

b) Right‑handed people do not find right‑hand threads easier to use (0.05<P<0.1).

c) Right‑handed people do not find right‑hand threads easier to use (P>0.1).

d) Right‑handed people find right‑hand threads easier to use (0.01<P<0.05).

Answer 1

1)

or each subject, randomly select which knob (right or left) that subject should use first.

2)

a) H0:μ=0

b) Ha:μ<0

subject ni (R-L) subject N. CR- - d m I so I sa -48 -43 - 12 most oooo= -16 -29 -3 -11 22 w 2 -16 38 in - 35 = - -45 -31 .nz Eu -13.32 , S = Elna) 2 n-1 22.936 t-statistic /s/un = -2.90 df: (n-1) = 24 p- valle: PA <-2.90) = 0.00393 (one sided test) Since the p-value is very close to o we have sufficient evidence to Reject the and conclude uco, i.e. Yes, right hand people find right hand threads easier to do. (sina p cool here) so option D. b correct