Question

[33] The manager of computer operations of a large company wants to study computer usage of two departments within the company - the accounting department and the research department. A random sample of five jobs from the accounting department in the past week and six jobs from the research department in the past week are selected, and the processing time in seconds) for each job is recorded: Department Processing Time (seconds) Accounting 93 8 712 Research 4 13 10 9 9 6 Use a level of significance of 0.05 (or 95% confidence) and use statistical inference (ie confidence intervals or hypothesis tests). a. [6] Estimate the mean processing time for all jobs in the accounting department b. [8] Is there evidence that the mean processing time in the research department is greater than 6 seconds? Include the error. C. [9] Is there evidence of a difference between the mean processing times of the accounting department and the research department? Assume that the variances are equal. Include the error. d. [5] Estimate the mean difference in processing times between the accounting and research departments. Assume a = 5%. e. [3] If the assumption of equal variances was not included, what would change in your calculations? f. [2] On the basis of the results, compose a short paragraph of your findings for the director of information systems concerning the two departments.

Answer 1

1. Suppose that the the accounting and research department. manager of computer operations of a large company wants to study computer usage of two departments within the company - Given the processing time (in seconds) for five jobs and size jobs in accounting and Research departosent respectively. Assume level of significance. a) To estimate : mean processing department d=0.05. The estimate of mean Sai, oth no time for all jobs in the accounting processing time for all jobs is given by h=ā= where, xo is processing time of a job in the accounting department n, is number of jobs in the accounting department = = = 9 +3+8+7+12 39 T = 39 = 7.8. Hoi M₂ <6 ť - paring where b) To test whether mean time in the research processing than 6 seconds. department (ple) is is greater The hypothesis to be tested are versus H : 41276. The test statistic is given by Jeg placunda Ho) t69-1), sample az is mean processing time of all jobs in research depeatme- is mean processing time on reseach department es sample standard deviation of research department is sarople jobs in research department. 5466 3.16/10 The critical value of t is to Co.05 )= 2.06 ant, 42 8r size of t-carve : 1.94. 0. On t=8.06

we The hypothesis are 54-es sp. Itt 2 do not reject Ho and conclude that MiFM2 There is no evidence of a difference between the mear processing Since t <telaos), do not reject Ho ot 2=0.05. We use upper (right2-tailed test as alternattve hypothesis, p>6. There is no evidence that H2>6. C) To test whether there is a difference between the mean poocessing times of an accounting department and the research 'department Assure equal variance Ho: Mi= M2 versus HI: M & Me The test statistic is given by t = ~ta +92-2) wheres sp is pooled variance and is given by SP = (n-1) 8² + (02-1) nithg-2 4x4.32+ 5*3.18 Sp ti = -0.31. 7.6.025) = 2.20 The costical value is given by tęco-025)'= 4, C43) * pater, bele can bee that t20.025) <t, tg10.025). Thus we fromes of the accounting department and the research department ' 5+6-2 t-Curve = 13.84.-) Sp = 3.72. 7.8 -8.5 ti = 3.72 V5 +/ 2/2=0.025 6 Wiesen - 2.26 = 2.26.

is st, stt tal d. Estimateon the mean difference in processing times between the Cocounting and Research department Assume a=s%. The estimate Puterval estimate of mean difference Mille given by Corth2-2) xSphe ItL 12 =) (7.5-8.5)+2.26* 3.72 *, *2*5+) = (-5.79,4.39),