Question

The manager for a large grocery store chain would like to determine if a new cash register will enable cashiers to process a larger number of items on average than the cash register which they are currently using. Seven cashiers are randomly selected, and the number of grocery items which they can process in three minutes is measured for both the old cash register and the new cash register. Thus, for the same 7 cashiers, you get two data values each. Assume that the differences between new and old data are normally distributed. Cashier Number of Grocery items processed in Three Minutes 1 2 3 4 5 6 60 70 55 75 62 52 65 71 55 - 65 57 7 8 OLD 5 NEW 75 57 a) Construct a 95% confidence interval for the population mean of the differences in the number of grocery items processed between the new and the old cash register.

Answer 1

Answer: Given dala, Number of Goocery itens pode cessed in three minutes casheir 2 3 4 5 6 7 OLD 60 70 55 75 62 52 58 NEW 65 71 55 75 65 57 57 Giren, n=7 a) 95-). CL for population mean diffrences. deg Jttc * Salin where n = 7 ā=edlo=13/7: 1.857 ~ 1.86 90 5 (0-3)/(2-1) 19 18 Degree of freedom, df = 0-1=7-1=6 critical value oft, te=2.447 :957. CI Pod popolation mean differences is -186 + 2.447 * 2.4815 -1.86+ 2.447 *0.9373 -(1.86€ 2.29) = (1-86-2.29, 1.86 +2.29) = 80 (-0.43, 4.15) :95% CI for population mean differences is lou3.4.15)

b) Here the confidence interval induce 'o'. There is not sufficient en evidence for the management to conclude that new co register Sill allow cashier to process a significan hy different number of items on average than the old register. Noll hypothesis: Ho: Md=0 Alternate hypothesis: Hald to Test Statistic: SONO 186 2.48/59 186 0.9373 -19844) R-Calcula P-value calculation: D- O n -1=6 . t: 198 P-value = T.DIST. 2T (1.98, 6) =/0.0950) comparison Given the level of significance is 54.20.05 since P-value>0.05, we fail to deject the null hypothesis. Here also there is not sufficient evédence for the managemeot to conclude that new cash register will allow cashier to process a Sigoificantly deeferent number of items on average than the d) we fail to reject null bypothesis on the basis of the test of significance. The error is, we retain the noll bypothesis which may be false in reality.

Here we made type I erooo conclude That is on the basis of test we might have wrongly conch that, there is no significant difference between process time and between new and old registers. But actually there may have been a difference. - thank you