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# Hypothesis Testing and Experimental Design

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Question 1.
As part of an internal audit of its bidding process, a company selected a random sample of 20 recently completed projects for review. One aspect concerned the procedure for estimating labour costs on projects. Data were collected on the estimated labour costs and the actual labour costs (in thousands of dollars) for these projects. Computer output for this analysis is included below.

Note: You should consider the design of this study to ensure the relevant output is analysed.

(a) What type of design is used in this study: Paired or two independent samples? Briefly justify.
(b) Briefly comment, in terms of the original story, on any of the features in the appropriate plot(s).
(c) What type of significance test is more appropriate for these data: Parametric or nonparametric? Briefly justify.
(d) Is there a difference, on average, between the actual labour costs and the estimated labour costs? Interpret all relevant results.

Question 2.
A lecturer of a large university paper is interested in whether attendance at class had an effect on students' final scores. The lecturer recorded the final scores from a random sample of 24 students who regularly attended class and 24 students who regularly skipped (did not attend) class. We wish to investigate whether there is a difference, on average, in final scores between students who regularly attended class and students who regularly skipped class. The data are displayed below:

(a) Using SPSS, draw the appropriate box plot(s) for this data set. (You should consider the design of this study to ensure the relevant plot(s) is drawn.) Comment on any features in the plot(s).
(b) Is there a difference between the underlying mean final scores for students who regularly attended class and that for students who regularly skipped class? Use SPSS to investigate this question. Interpret your results.
(c) Is it possible to claim that, on average, the difference in final scores for students is due to class attendance? Briefly explain.

***Please see the attached file (Statistics 2.doc) for the complete assignment.***

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#### Solution Preview

Question 1.

As part of an internal audit of its bidding process, a company selected a random sample of 20 recently completed projects for review. One aspect concerned the procedure for estimating labour costs on projects. Data were collected on the estimated labour costs and the actual labour costs (in thousands of dollars) for these projects. Computer output for this analysis is included below.

Note: You should consider the design of this study to ensure the relevant output is analysed.

(a) What type of design is used in this study: Paired or two independent samples? Briefly justify.

This is a paired study, because each project in the sample gave us two data points (we have an estimated cost and an actual cost from each project). This means that the data from the two samples (the estimated and actual costs) can be paired by pairing up the data points that came from the same project.

To be a paired study, the data would have to come from two independent populations. Since the data came from the exact same population, they are not independent.

(b) Briefly comment, in terms of the original story, on any of the features in the appropriate plot(s).

From the box-plots: The minimums, 1st quartiles, medians, and 3rd quartiles of the actual and estimated ...

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