Part of a usability study to assess voting machines measured the time on task (TOT) of voters casting ballots (efficiency). Specifically, the data are for the same ballot cast on two different voting machines at the same location (called a precinct). Your job is to perform a "t" test on these data and draw conclusions about which voting machine is better in terms of usability. A few background items:
The voters (participants/users) are a homogeneous group.
Voters were randomly assigned to the voting machines.
Thus, the two groups of voters (one group using the DRE voting machine, and the other using the OptiScan voting machine) have equal variances.
We have no advance information to indicate that one voting machine will be better than the other.
You do not need to do any hand calculations. Use the following site as it has a very easy to use "t" test calculator:
DREOptiScan
532
513
573
500
880
757
956
461
430
512
998
651
349
754
610
623
615
1185
528
497
718
648
589
421
490
591
758
776
498
498
623
621
594
594
602
458
567
865
546
714
729
785
581
804
661
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251
810
572
499
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391
354
650
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358
463
321
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181
285
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261
292
366
359
398
806
380
954
344
375
356
399
383
464
618
524
304
342
576
277
390
818
387
645
Question1 – What is the null hypothesis in this usability study?
Question 2 – How many degrees of freedom are in each group (the DRE and OptiScan groups)?
Question 3 – Which "t" test should be used – paired, unpaired/equal variance, unpaired/unequal variance?
Question 4 – Should a one-tail, or two-tailed test be used, and why?
Question 5 – What is the t value?
Question 6 – Is the t value significant at the 0.05 level, and why?
Question 7 – Is the t value significant at the 0.01 level, and why?
Question 8 – Considering the combination of the above analysis, and the number of ballots completed which voting machine has better usability, and why?