A supermarket manager is examining whether a new plastic bagging configuration i

Question

A supermarket manager is examining whether a new plastic bagging configuration in the produce area might make it more efficient for customers who are bagging their own fruits and vegetables. She observes a sample of customers using the new system and a sample of customers using the standard system, and she notes how many seconds it took each of them to unroll and open the plastic bag in preparation for bagging the veggies. The data are in le XR11098. Considering these as data from independent samples, use the 0.05 level of significance in examining whether the population mean for the new bagging system might be less than that for the conventional system. Identify and interpret the p-value for the test.

new standard 8.1 10.5 9.4 9.5 11.1 9.9 10.3 10.7 11.2 13.3 10.8 8.5 7.8 9.1 7.0 9.6 10.4 10.8 9.2 10.2 9.3 9.0 7.0 8.3 8.8 9.3 7.7 11.2 8.1 7.8 9.0 10.1 12.1

Explanation / Answer

Step :I Null Hypothesis : H0 : There is no difference in the population mean for the new bagging systyem and the conventional system. new = conventional

Alternative HYpothesis : Ha : population mean for the new bagging system is significantly lesser than that for the conventional system. new < conventional

Step II : Significance level Alpha = 0.05

Step III: Test statistic

dF = 18 + 15 -2 = 31

pooled variance sp2 = [ ( n1 -1) s1 2 +  ( n2 -1) s2 2] / (n1 +n2 -2) =(17 * 2.26 + 14 *1.864) / 31 = 2.0812

Test statisitc

t = (x1 - bar - X2- bar)/ sqrt [ sp2 (1/n1 + 1/n2 )] = (9.3- 9.85)/ sqrt [2.0812 * ( 1/ 18 + 1/15) ] = - 0.55/ 0.5043 = -1.09

tcritical for dF = 29 and alpha = 0.05 is equal to and left tailed test is = 1.6955

P - value = Pr ( (x1 - bar - X2- bar) <= -0.55 ; 0 ; 0.5043 ) = 0.1434 ( from t - table for p - value)

so we can not reject the null hypothesis as p - value is not under significane value and we conclude that there is no significant difference in mean for new bagging sytem then the conventional one.

new standard Mean 9.3 9.846667 Variance 2.26 1.864095 Observations 18 15 Pooled Variance 2.0812 Hypothesized Mean Difference 0 df 31

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