Question

4. Paulina Borden, an IE for One Percent Bank, recently completed a simulation of the process used to distribute money to Automated Teller Machines (ATMs). Her simulation modeled the armored vehicles as they left the bank and visited the 20 ATMs in the region. In the original system she modelled the existing behaviour exactly. The existing behaviour sees the drivers use the same route regardless of the time of day. This means the armored vehicles often get stuck in traffic jams. She wants to compare the original system to the following proposed system. In the proposed system the routes used by the armored vehicles will be different at different times of the day and will be chosen in an effort to avoid traffic jams. a) Should a paired t-test be used to compare the results from the original system to the proposed system? Explain why or why not. b) Use the following data and determine if the proposed system should be adopted or not assume 90% confidence and two independent samples with equal variance). The data represents the minutes needed to complete a single route. Replication 172 Original Proposed 177 175 186 172 188 172 186 189 188 184 170 173 166 180 186 172 177 182 170

Answer 1

A)

Yes a paired t test can be used to compare the results.

Like any other statistical procedure, the paired sample t-test has a null hypotheses and an alternative hypotheses.

If the null hypotheses is true then the true mean differences between then paired sample is zero.
If the alternative hypotheses is true then the true mean difference between the paired sample is not zero,

It might be greater than or lower than zero. Namely upper limited and lower limited. An upper-tailed or lower-tailed hypothesis can be used to increase the power of the test. The null hypothesis remains the same for each type of alternative hypothesis.

• • The null hypothesis (Mo) assumes that the true mean difference (μd) is equal to zero.
• • The two-tailed alternative hypothesis (M1) assumes that μd is not equal to zero.
• • The upper-tailed alternative hypothesis (M2) assumes that μd is greater than zero.
• • The lower-tailed alternative hypothesis (M3) assumes that μd is less than zero.

2)

Replication	Original	Proposed	Difference (O-P)	(O-P)^2
1	177	175	2	4
2	186	172	14	196
3	188	172	16	256
4	172	186	-14	196
5	189	188	1	1
6	184	170	14	196
7	173	166	6	36
8	180	186	-6	36
9	172	177	-5	25
10	182	170	12	144
Total			40	1090

t =

«ΣD) /N)/Σ D2 – ΣD?)/N))/(N – 1)(Ν)

Using this formula where: -

D = difference

N = Number of samples

we get t = 3.3

Given confidence level = 90%

The difference will be +- 0.10

Use T table to find out the value.