[SOLVED] Excel assembly 1

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ETB2111 Assessment Task 2: Assignment 1

Semester 1 2017

Due date: 3rd May 2017 (Wednesday of Week 9) by 4 pm

Topics: Comparing 2 population means & proportions and the Chi-squared tests

Assessment Weight: 10%

This assignment consists of 3 questions.

All relevant Excel outputs must be labelled clearly and made part of the answers to

support your explanations. Please make sure that a graph, table or Excel output for a

model appears on a single page and not divided between pages. You may annotate

these outputs for clarity.

The data file for this assignment is provided in file Ass1-2017data.xls placed in

Assignment 1 section on the home page of ETB2111 in Moodle.

Submit this assignment in print form, attaching a signed cover sheet. Please use the

cover sheet placed in Moodle.

ASSIGNMENTS WITHOUT SIGNED COVER SHEETS WILL NOT BE ACCEPTED.

DO NOT SUBMIT DISCS or USBs with the printed copy of the assignment.

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Note: In answering parts of the questions where statistical inference is required, you must include

some or all of the following (as appropriate) for full credit:

1. the reason for using a particular formula or distribution

2. the null and alternative hypotheses

3. the critical value(s) used

4. the level of significance

5. the distribution of the statistic employed in a test, and

6. the conclusion.

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Question 1 (2+7+3 = 12 marks)

The traffic regulatory authority in a big city conducted an experiment to compare the mean reaction

time to two types of traffic signs, prohibitive (No Left Turn) and permissive (Left Turn Only). Ten

drivers were included in the experiment. Each driver was presented 40 traffic signs, 20 prohibitive

and 20 permissive, in random order. The mean reaction time and the number of correct actions

were recorded for each driver. The mean reaction times to the 20 prohibitive and 20 permissive

traffic signs are shown below (Table 1) for each of the ten drivers. The data are provided in file Ass1-

2017data.xls.

Mean reaction times (micro
seconds) for 20 traffic signs

Driver Prohibitive Permissive

1 824 702

2 866 725

3 841 744

4 770 663

5 829 792

6 764 708

7 857 747

8 831 685

9 846 742

10 759 610

Table 1

(a) On the basis of the purpose of the experiment and the data collection method explained

above, would an independent samples or paired samples design be more useful in

understanding information on the difference between reaction times to prohibitive and

permissive traffic signs? Explain the reason for your choice.

(b) Using the critical value approach and 1% level of significance, perform an appropriate test to

determine if the data present sufficient evidence to indicate a difference in mean reaction

times to prohibitive and permissive traffic signs. Give all relevant details to support your

answer. You may use Excel or apply the test manually.

(c) Find a 99% confidence interval estimate for the difference in the mean reaction times to

prohibitive and permissive traffic signs. Does the estimated CI support your conclusion in part

(b)? Explain.

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Question 2 (2+3+4+7+2 = 18 marks)

The director of training for a company manufacturing electronic equipment is interested in

determining whether different training methods have an effect on the average time it takes an

assembly-line employee to complete a job.She randomly assigned the 42 recently hired employees

for the assembly-line to two equal sized groups.One group received a computer-assisted individual-

based training, while the other group received a team-based training program.Upon completion of

the training program, the employees were evaluated on the time (in seconds) it took to assemble a

part.The data on assembly times are displayed in Table 2 and given in file Ass1-2017data.xls.

Computer-Assisted, Individual-

based Program Team-based Program

19.4 17.7 16.5 22.4 17.1 23.7

16.7 16.1 17.7 13.8 18 17.4

20.7 19.8 16.2 18.7 28.2 23.2

19.3 16.8 17.4 18 21.7 20.1

21.8 19.3 16.4 19.3 20.8 12.3

16.8 14.7 16.8 20.8 30.7 15.2

14.1 16 18.5 15.6 24.7 16

Table 2

(a) On the basis of data collection method used in the given study, explain whether an

independent or a dependent samples design would be suitable for comparing the average

assembly times of workers trained by the two methods in this problem.

(b) Find the means and the variances of the assembly times for the two groups of employees to

2 decimal places. Do the means and variances look similar?

(c) Using a 0.05 level of significance, perform a test to check the equality of variances in

assembly times of employees trained by the two training programs. Your answer must

include relevant hypotheses and the value of the test statistic, the formula for the test

statistic, conclusion and interpretation of your result.

(d) Keeping in view the conclusion from part (c), obtain a 95% confidence interval estimate for

the difference between the average assembly times of employees trained by the two

training methods.Interpret this confidence interval estimate.

(e) On the basis of 95% confidence interval obtained in part (d), can we conclude that there is

no difference in the mean assembly times of the two training methods?Explain the reason

for your answer.

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Question 3 (2 + 6 + 2 = 10 marks)

When a new product is introduced in a market, the period following its distribution is very critical to

its performance. It is, therefore, important for the manufacturer to evaluate the products

performance during this critical period. A study of market penetration, as it is called, involves

sampling consumers and assessing their exposure to the product. The manager of the marketing

division of a company believes that the extent of market penetration depends on the city selected

for study. To verify his belief, he selects random samples of 200 and 150 consumers from cities 1 and

2, respectively, and collates the consumer responses as displayed in Table 3.1. His calculations of the

proportions of consumer responses regarding the exposure to the product for each city are reported

in Table 3.2.

Never heard of the

product

Heard about it but

did not buy

Bought it at least

once

Total

City 1 36 55 109 200

City 2 45 56 49 150

Total 81 111 158 350

Table 3.1

a. Showing all steps, and using 5% significance level and the critical value approach, test

whether the extent of market penetration varies with the city.

b. What are some of the limitations (i.e., requirement) on the use of the test that you apply in

part (b)? Did you need to compromise on these limitations for using the test? Explain briefly.

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