Question

1. [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 9 3 8 7 | 12 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

Answer 1

time @ Mean processing for all jobs in the accounting dept sum of observation nop all observations Total no. - 9+ 3 + 8 + 7 + 12 39 - 5 5 5 7-8 seconds ce If assumption equal variances is not included, We would use the unpooled it test here For the accounting dypt, For the research cept, X2 = 8.5 si = 3.271 S₂ m=6 Test statistic Cto) Xi - X2 Xi - 7.8 3.146 m = = 5 7.8 - 805 il calcio 2 13.2712 + 3.1462 5 6 Test statistic (to) = -0-360 2 2 2 df (v) = + so N2 + 3,044) (3.2712 3.1464 5 8, 2/22) ² (3.272/5)² N27 4 (57/2,² ni-1 (6271) 51° (3.142013 + df Cv) 8 Capprouimately) n

the critical value q If it is a-sided at test tazgr = t 0.025,8 2.306 If it is I-sided t test the critical value:- taqv 1.860 to.os, 8 Sounce of critical valey- STATKEY Cimaye attached) ] 9 So, if the assumption of equal variance is not included, the test statistic a degrees of freedom and the critical value what vary and depending upon the hypothesis test is (a-sided or I-sided), vary. will p-value will also

StatKey Theoretical Distribution T Distribution- Reset Plot T Distribution Left Tail Two-Tail Right Tail 0.40 df 8 0.35 Edit Parameters 0.30 0.25 0.20 0.025 0.950 0.025 0.15 0.10 0.05 0.00 -4 -3 -2 -1 0 1 2 -2.306 2.306 Activate Windows

Statkey Theoretical Distribution T Distribution- Reset Plot T Distribution Left Tail Two-Tail Right Tail 0.40 df 8 0.35 Edit Parameters 0.30 0.25 0.20 0.050 0.15 0.10 0.05 0.00 -2 -1 0 1 1.860 Activate Windows

The mean is found using the formula mentioned. Incase equal variances is not considered , we use the unpooled t test. So the test statistic , degrees of freedom, critical values and the p value will also vary depending on whether the hypothesis test is 2 sided or 1 sided.The calculations using the formula mentioned has been shown. The critical values for the one sided and 2 sided hypothesis test is obtained from STATKEY (image attached for reference).