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ADM 2304 – ASSIGNMENT 2 (Week 3-4-5-6)

2022

Question 1. [ 30 marks]

A Human Resource director of a large company wants to investigate if professional staff takes longer coffee breaks than their technical counterparts. She takes a random sample of 10 professionals and another sample of 10 technicians in the company and determines via their supervisors the amount of time (in minutes) they spent for the coffee breaks during a specific day. The results are available in the Assign2Data.xlsx file., answer the following questions.

(a) Assess whether the assumptions/conditions for performing a two-sample t-test to compare break time between the two groups of employees are warranted (justify your answers). [4]

(b) Irrespective of your answer in (a) above, test at 5% level of significance whether the professional employees take longer coffee breaks than their technical counterparts. Assume the two population variances are the same and use both the critical value and pvalue approaches (using approximate values from t distribution table). Show all the steps of your hypothesis test (hypotheses, significance level, test statistic, decision criteria, critical value, p-value, decision with justification). (Manual Calculations) [10]

(c) Build an appropriate confidence interval to support your results in (b) above; is this confidence interval consistent with your conclusion? (Manual Calculations) [4]

(d) Irrespective of your answer in (b) above, now perform an appropriate nonparametric test at a 5% level of significance. Clearly state hypotheses, significance level, test statistic, decision criteria and conclusion. Also, verify your calculations with StatCrunch output. (Manual Calculations and StatCrunch output) [10]

(e) Which test is more appropriate in this situation? Justify your answer. [2]

Question 2. [ 25 marks]

A polling company wants to test the time (in minutes) required to run two different versions of a new survey questionnaire to prepare costing options for its client. They select a random sample of 9 respondents and administer version A to them. A week later, they recontact the same respondents and administer them version B. The results (in minutes) to complete the two versions of the questionnaire for each respondent is presented in the Assign2Data.xlsx file.

(a) Which approach is more appropriate to analyse these data - a paired data approach or two independent samples approach? Explain. [2]

(b) Explain whether a parametric or nonparametric test is more appropriate to test if Version A takes longer time to administer than Version B (mean or median?). [2]

(c) Ignoring your response in (b), perform an appropriate parametric test to see whether there is enough evidence at a 5% level of significance to show that Version A takes more time on average to complete than Version B. Show your detailed manual calculations and all the steps of your hypothesis test (hypotheses, significance level, test statistic, decision criteria, critical value, decision with justification). (Manual Calculations) [10]

(d) Now, still ignoring your response in (b), perform an appropriate nonparametric test at a 5% level of significance. Clearly state hypotheses, significance level, test statistic, decision criteria, and conclusion. (Show your manual calculations and show your StatCrunch output) [10]3

Question 3. [ 20 marks]

The following table shows the ethnic origins of two random samples of students from a Canadian university, one from 2012 and the other from 2022:

                       European     Asian     African     Other

             2012      308           58         22           52

             2022      364           100        38           58

Note: Canadian born students are classified according to their ancestry.

(a) What would be an appropriate test to check if there has been an overall change in the distribution of ethnic origins among the student population of that university between 2012 and 2022? Justify your answer. [2]

(b) Based on your answer in (a) above, test whether there has been an overall change in the distribution of ethnic origins among the student population of that university between 2012 and 2022. Use a 5% significance level and show your detailed manual calculations and all the steps of your hypothesis test (hypotheses, significance level, expected cell frequencies (rounded to 1 decimal), test statistic, decision criteria, critical value and p-value, conclusion with justification). (Manual Calculations) [10]

(c) Now, suppose you want to test whether the distribution of ethnic origin among this student population in 2022 was consistent with the following ratios for all Canadian universities in 2022: European 75%, Asian 10%, African 5%, and other 10%. Use StatCrunch and conduct an appropriate test using a 1% significance level and report your hypothesis, test statistic, decision criteria (using p-value) and conclusion (Show your detailed StatCrunch Output). [8]