Every month a clothing store conducts an inventory and calcu

Every month a clothing store conducts an inventory and calculate losses from theft. The store manager wants to see if using a security guard helps reduce theft (and thus warrants his or her paycheck) versus using a security camera. The following monthly loss data was collected during periods of guard usage vs. camera usage. Test the hypothesis that (Camera)-(Security Guard)>0 at the 5% significance level (assuming that the underlying population of monthly losses is approximately normally distributed) under the following assumptions: (A) Equal variances (B) Unequal variances (C) Do the results agree? Security guard losses: $355, 284, 401, 398, 477, 254 Camera losses: $486, 303, 270, 386, 411, 435

Solution

Let X1 and X2 denote the camera usage and gaurd usage. Given n1=n2=6, from the given data x1bar=381.8333, x2bar=361.5, s1=74.4612, & s2=75.0972. Ho: 1=2, i.e., there is no significant difference between the means among camera usage and gaurd usage. H1:1>2 , i.e., it is right tail test. The table value of Z at 5% level of significance for right tail test is 1.645. (a):Equal variances: then Zcal=(x1bar-x2bar)/[([(1/n1)+(1/n2)])], where ²=(n1s1²+n2s2²)/(n1+n2). Zcal=(381.8333-361.5)/[(74.7799)*((0.3333))]=20.3333/43.1704=0.710< Ztab, so we accept Ho. (b):unequal variances: Zcal=(x1bar-x2bar)/[[(s1²/n1)+(s2²/n2)]=(381.8333-361.5)/(924.0784+939.9316)=20.333/43.1742=0.471<Ztab, so we accept Ho. Therefore, Ho: 1=2, i.e., there is no significant difference between the means among camera usage and gaurd usage. . (c): the results does not agree in two cases.