Question

STATE: The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking 2525 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 2525 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
11	113113	137137	1414	107107	8787
22	105105	105105	1515	118118	166166
33	130130	133133	1616	103103	146146
44	101101	108108	1717	111111	123123
55	138138	115115	1818	104104	135135
66	118118	170170	1919	111111	112112
77	8787	103103	2020	8989	9393
88	116116	145145	2121	7878	7676
99	7575	7878	2222	100100	116116
1010	9696	107107	2323	8989	7878
1111	122122	8484	2424	8585	101101
1212	103103	148148	2525	8888	123123
1313	116116	147147

To access the complete data set, click the link for your preferred software format:

Excel  Minitab  JMP  SPSS TI  R  Mac-TXT   PC-TXT  CSV CrunchIt!

(a) Each of the 2525 students used both instruments. Select the correct explanation describing how randomization works in arranging the experiment.

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

For each knob, randomly select which student will turn it.

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

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

PLAN:

(b) 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.

?0:?=0H0:μ=0

??:?≠0Ha:μ≠0

?0:?=0H0:μ=0

??:?>0Ha:μ>0

?0:?≤0H0:μ≤0

??:?>0Ha:μ>0

?0:?=0H0:μ=0

??:?<0Ha:μ<0

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

33	88
22	0 30 3
11	11
00	22
−0−0	7 4 3 3 1 07 4 3 3 1 0
−1−1	6 6 6 2 16 6 6 2 1
−2−2	9 49 4
−3−3	5 1 15 1 1
−4−4	8 5 38 5 3
−5−5	22
−6−6

33
22	1 51 5
11	0 1 3 80 1 3 8
00	0 1 3 3 4 70 1 3 3 4 7
−0−0	6 6 6 2 16 6 6 2 1
−1−1	9 4 1 19 4 1 1
−2−2	5 5 35 5 3
−3−3	8 28 2
−4−4
−5−5
−6−6

33	88
22	0 30 3
11	11
00	22
−0−0	22
−1−1	2 12 1
−2−2	44
−3−3	6 6 6 5 1 16 6 6 5 1 1
−4−4	9 8 5 4 39 8 5 4 3
−5−5	7 4 3 3 1 07 4 3 3 1 0
−6−6

33	0 1 1 3 3 3 7 80 1 1 3 3 3 7 8
22	0 1 1 40 1 1 4
11	6 6 66 6 6
00	1 1 4 5 5 91 1 4 5 5 9
−0−0
−1−1	2 12 1
−2−2
−3−3	33
−4−4	8 28 2
−5−5
−6−6

SOLVE: Calculate the mean ?¯x¯ and standard deviation, ?s. (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

?¯=x¯=

?=s=

Calculate the ?t‑statistic. (Enter your answer rounded to two decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

?=t=

Find the degrees of freedom, dfdf . (Enter your answer as a whole number. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

df=df=

What is the ?P‑value. (Enter your answer rounded to four decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

?=P=

CONCLUDE: What is your conclusion?

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

Right‑handed people do not find right‑hand threads easier to use (0.05<?<0.10.05<P<0.1).

Right‑handed people find right‑hand threads easier to use (0.01<?<0.050.01<P<0.05).

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

Answer 1

Solution:

Given data is calculated in excel .