Question

Question: An army depot that overhauls ground mobile radar systems is interested in improving its processes... An army depot that overhauls ground mobile radar systems is interested in improving its processes. One problem involves troubleshooting a particular component that has a high failure rate after it has been repaired and reinstalled in the system. The shop floor supervisor believes that having standard work procedures in place will reduce the time required for troubleshooting this component. Time (in minutes) required troubleshooting this component without and with the standard work procedure is recorded for a sample of 19 employees The sample mean difference in time was -25 minutes with a sample standard deviation of 2 minutes. Does this sample indicate that having a standard work procedure in place reduces troubleshooting time?

Answer 1

Null Hypothesis H0 :  Mean difference in time (in minutes) required for troubleshooting the component without and with the standard work procedure is 0.

Alternative Hypothesis Ha :  Mean difference in time (in minutes) required for troubleshooting the component without and with the standard work procedure is less than 0.

Sample mean difference = -25

Hypothesized mean difference = 0

Standard error of mean difference = sd / = 2 = 0.4588

Test statistic, t = (Sample mean difference - Hypothesized mean difference) / Standard error

= (-25 - 0) / 0.4588

= -54.49

Degree of freedom = n - 1 = 19 - 1 = 18

P-value = P(t < -54.49) = 0

Since p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that mean difference in time (in minutes) required for troubleshooting the component without and with the standard work procedure is less than 0. Thus, the sample indicate that having a standard work procedure in place reduces troubleshooting time.