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 n =30 iterations of the program are given below. 38.65 44.06 41.47 35.64 33.05 40.85 41.28 34.11 34.05 43.16 36.66 37.66 44.92 39.13 47.01 39.36 43.05 37.45 51.11 45.72 38.18 35.04 40.97 47.89 37.96 37.28 43.28 31.92 34.87 37.53 (a) Based on these data, construct a 95% confidence interval for the average running time of the program. (b) Test the claim that the average running time of the program is 40 seconds, using a significance level of α =0.05. Use the hypotheses H0 : µ =40s and HA : µ 6=40s.

Answer 1

a)
sample mean, xbar = 39.85
sample standard deviation, s = 4.7724
sample size, n = 30
degrees of freedom, n - 1 = 29

For 0.95 Confidence level, the t-value = 2.05
CI = (xbar - t*s/sqrt(n), xbar + t*s/sqrt(n))
CI = (39.85 - 2.05 * 4.7724/sqrt(30) , 39.85 + 2.05 * 4.7724/sqrt(30))
CI = (38.06 , 41.64)

b)
As 40 is included in the above calculated CI, we fail to reject the null hypothesis
there are not significant evidence to conclude that the average running time of the program is different than 40 seconds,