. Each employee hired at an electronics parts assembly line in Edmonton, Alberta
ID: 3150421 • Letter: #
Question
. Each employee hired at an electronics parts assembly line in Edmonton, Alberta, is given a general intelligence test. To determine which method of training is more effective, eight pairs of new hires were matched according to their exam scores. One set of employees was asked to read appropriate training manuals, while the other group watched interactive training videos. Each employee was then asked to assemble a part used in a locater-beacon transmitter, and the time (in minutes) to completion was recorded. The summary data are given in the following table.
(1 pt.) a) Should this situation be analyzed via a 2-sample independent or paired method? Please explain your answer.
(6 pts.) b) Is there any evidence to suggest the true mean time difference is different from 0? Assume normality and use = 0.01. Remember to include the complete 4-step method in the hypothesis test.
(2 pts.) c) Calculate and interpret the appropriate confidence interval or bound.
(1 pt.) d) In practical terms, does the data imply that the true mean time difference is different from 0? This part uses the information from parts b) and c), however, if no addition reasoning is provided, you will receive 0 points.
Explanation / Answer
(1 pt.) a) Should this situation be analyzed via a 2-sample independent or paired method? Please explain your answer.
Data are paired according to exam scores, so PIRED METHOD. [ANSWER]
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(6 pts.) b) Is there any evidence to suggest the true mean time difference is different from 0? Assume normality and use = 0.01. Remember to include the complete 4-step method in the hypothesis test.
Formulating the null and alternative hypotheses,
Ho: ud = 0
Ha: ud =/ 0
As we can see, this is a two tailed test.
Thus, getting the critical t,
df = n - 1 = 7
tcrit = +/- 3.499483297
Getting the test statistic, as
X = sample mean = 0.5875
uo = hypothesized mean = 0
n = sample size = 8
s = standard deviation = 0.9687
Thus, t = (X - uo) * sqrt(n) / s = 1.715392728
As |t| < 3.499, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant difference between the mean scores of the two methods. [CONCLUSION]
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(2 pts.) c) Calculate and interpret the appropriate confidence interval or bound.
We compute a 1-0.01= 0.99 confidence interval.
Note that
Margin of Error E = t(alpha/2) * s / sqrt(n)
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 0.5875
t(alpha/2) = critical t for the confidence interval = 3.499483297
s = sample standard deviation = 0.9687
n = sample size = 8
df = n - 1 = 7
Thus,
Margin of Error E = 1.198528129
Lower bound = -0.611028129
Upper bound = 1.786028129
Thus, the confidence interval is
( -0.611028129 , 1.786028129 ) [ANSWER]
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(1 pt.) d) In practical terms, does the data imply that the true mean time difference is different from 0? This part uses the information from parts b) and c), however, if no addition reasoning is provided, you will receive 0 points.
NO. As we can see, we failed to reject Ho in part b, and 0 is inside the interval in part c. Hence, there is no significant evidence that the true mean time difference is different from 0. [CONCLUSION]
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