Question

Right versus left. The design of controls and instruments affects how easily people can use them. Timothy Sturm investigated this effect in a course project, 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). Table 20.4 gives the times in seconds each subject took to move the indicator a fixed distance.33 DATA RTLFT

(a) Each of the 25 students used both instruments. Explain briefly how you would use randomization in arranging the experiment.

Answer 1

SOLUTION:

a. Assign every individual a number 01-25. Use a random number table to select 12 (or13) of the individuals to try the right thread first, while the other group would try the left thread first. After a break, switch threads and repeat the experiment.

Here we have to test the hypothesis that,

H0 : muR-L = 0 Vs H1 : muR-L < 0

Here we use paired t-test because there are two observations on one subject.

Assume alpha = 0.05

Paired t-test in MINITAB :

ENter data into MINITAB sheet --> Stat --> Basic Statistics --> Paired t --> Samples in columns --> First sample : select Right thread data --> second sample : select left thread data --> Options --> Confidence level : 95.0 --> Test mean : 0.0 --> Alternative : less than --> ok --> ok

Output :

Paired T-Test and CI: Right thread, Left thread

Paired T for Right thread - Left thread

N Mean StDev SE Mean
Right thread 25 104.120 15.796 3.159
Left thread 25 117.440 27.263 5.453
Difference 25 -13.3200 22.9360 4.5872

95% upper bound for mean difference: -5.4718
T-Test of mean difference = 0 (vs < 0): T-Value = -2.90 P-Value = 0.004

Test statistic = -13.32 - 0 / (22.936/sqrt(25)) = -2.90

P-value = 0.004

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : There is statistically significant evidence to support the hypothesis that right-handed people find right-hand threads easier to use.