Question

In: Statistics and Probability

Right versus left. The design of controls and instruments affects how easily people can use them....

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.

Expert Solution

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.

orchestra answered 2 years ago

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