Question

An educator has written a computer program to automate a repetitive task. Due to the nondeterministic nature of the task, the program takes various amounts of time to run. The running times, in seconds, of six iterations of the program are given below. 38.65 44.06 41.47 35.64 33.05 40.85
Based on these data, construct a 95% confidence interval for the running time of the program.

Answer 1

= (38.65 + 44.06 + 41.47 + 35.64 + 33.05 + 40.85)/6 = 38.953

s = sqrt(((38.65 - 38.953)^2 + (44.06 - 38.953)^2 + (41.47 - 38.953)^2 + (35.64 - 38.953)^2 + (33.05 - 38.953)^2 + (40.85 - 38.953)^2)/5) = 4.0479

At 95% confidence interval the critical value is t^* = 2.571

The 95% confidence interval is

+/- t^* * s/

= 38.953 +/- 2.571 * 4.0479/

= 38.953 +/- 4.2487

= 34.7043, 43.2017