Question

11. (13 pts) A systems specialist has studied the work-flow of clerks who do the same inventory work. Based on this study, she designed a new work-flow layout for the inventory system. To compare average production for the old and new methods, she took a random sample of six clerks. The average production rate number of inventory items processed per shift) for each clerk was measured both before and after the new system was introduced. The results are shown below. Test the claim that the new system increases the mean number of items process per shift. Use a = 0.05. Clerk 1 2 3 4 5 Old 11610893 119 111 New 122 114 112 127 122 a State the null and alterate hypotheses. Is the test left-tailed, right-tailed, or two- tailed? b. Identify the appropriate sampling distribution: the standard normal or the Student's 1. What is the value of the sample test statistic? c. Find or estimate the P-value. d. Based on your answers for parts (a) through (c), will you reject or fail to reject the null hypothesis?

Answer 1

Using Excel, go to Data, select Data Analysis, choose t-Test: Two-Sample Assuming Unequal Variances.

	Old	New
Mean	105.500	113.333
Variance	169.100	267.867
Observations	6	6
Hypothesized Mean Difference	0
df	10
t Stat	-0.918
P(T<=t) one-tail	0.190
t Critical one-tail	1.812
P(T<=t) two-tail	0.380
t Critical two-tail	2.228

a. H₀: µ₁ > µ₂, New system does not increase the mean number of items process per shift

H₁: µ₁ < µ₂, New system increases the mean number of items process per shift

Left-tailed

b. Student's t

Test statistic = -0.918

c. p-value = 0.190 (one-tail)

d. Since p-value is more than 0.05, we fail to reject the null hypothesis.

So, new system does not increase the mean number of items process per shift.