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InferenceScenarios_2013

6 scenario 8 design of controls the design of

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Scenario 8. Design of Controls 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 actions. 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 data give the times required (in seconds) to move the indicator a fixed distance: Su bje ct 1 2 3 4 5 6 7 8 9 10 11 12 13 Ri gh t Th re ad 11 3 10 5 13 0 10 1 13 8 11 8 87 11 6 75 96 12 2 10 3 11 6 Le ft Th re ad 13 7 10 5 13 3 10 8 11 5 17 0 10 3 14 5 78 10 7 84 14 8 14 7 Su bje ct 14 15 16 17 18 19 20 21 22 23 24 25 Ri gh t Th re ad 10 7 11 8 10 3 11 1 10 4 11 1 89 78 10 0 89 85 88 Le ft Th re ad 87 16 6 14 6 12 3 13 5 11 2 93 76 11 6 78 10 1 12 3 The project hoped to show that right-handed people find right-hand threads easier to use. State the appropriate null and alternative hypotheses about the mean time required to complete the task and carry out a hypothesis test at the usual 5% significance level. Be sure to compute a P-value (use Excel to do this). Then report your conclusions. SOLUTION: This is a matched-pairs t-test. H 0 : μ d = 0 (or μ R – μ L = 0) H a : μ d < 0 (or μ R – μ L < 0) = -13.32; s d = 22.936; t-stat = -2.904 Using 24 degrees of freedom, the one-tailed P-value is 0.0039. Conclusion: There is strong evidence that the time to complete the task is less for the right-hand threads than the left-hand threads. The difference is statistically significant. 7
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*** 95% confidence interval for the mean time advantage of right-hand over left-hand threads. The 95% confidence interval for the mean time advantage is: -13.32 ± 2.064(22.936/√25) = -13.32 ± 9.47 or (-22.79, - 3.85) Do you think that the time saved would be of practical importance if the task were performed many times – for example, by an assembly-line worker? To help answer this question, find the mean time for right-hand threads as a percent of the mean time for left-hand threads. The ratio of mean time for right-hand threads as a percent of mean time for left-hand threads is = 88.7%, so those using the right-hand threads complete the task in about 90% of the time it takes those using the left-hand threads. 8
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Scenario 9. Supervisory Structure and Job Satisfaction A management behaviour analyst has been studying the relationship between male/female supervisory structures in the workplace and the level of employees’ job satisfaction. The results of a recent survey are shown in the following table. Boss/Employee Level of Satisfaction Female/Male Female/Female Male/Male Male/Female Satisfied 21 25 54 71 Neutral 39 49 50 38 Dissatisfied 31 48 10 11 Convert the table of counts to a table of column percentages. Rank the four boss/employee gender relationships from highest to lowest in terms of percent satisfied.
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