Question

The owner of chain retails stores wished to compare the number of shoplifters in her stores for a one month period prior to the installation of a new security system to the number of shoplifters in the same stores for a one month period after the security system was installed. Shes not sure if the new system will increase for a one month period after the security system was installed. Shes not sure if the new system will decrease shoplifters or actually increase the number of shoplifters. She hires you to assess whether the new security system has changed the number of shoplifters. The data are as follows:

Store	Old Security System	New Security System
1	26	24
2	18	19
3	19	18
4	30	26
5	22	25

1. Why is this a dependent samples t-test and not an independent samples t-test

2. State the null and alternative hypotheses in sentence from and using symbols

3. What is the critical value of t that you would have to reach in order to reject the null hypothesis

4. Conduct a t-test to determine the actual value of t for this data

5. Would you reject or fail to reject the null the hypothesis?

Calculate the value of r2 ( r square) for this data

7. Based on your result (of both the hypothesis test as well the result of r2 (sq)), what you recommend to the store owner.

Answer 1

1. it is the same group of cases

So we use a dependent samples t-test

6)

	X	Y	X*Y	X^2	Y^2
	26	24	624	676	576
	18	19	342	324	361
	19	18	342	361	324
	30	26	780	900	676
	22	25	550	484	625
Sum =	115	112	2638	2745	2562

The value of R is 0.85.

This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).

The value of R², the coefficient of determination, is 0.7225.

7)

72.25% variation in the Y variable is predictable from X variable

Y = New Security System

X = Old Security System