An efficiency manager is evaluating the quality of sportswear manufactured by two brands - A and B. She wishes to test whether the difference between the mean number of faulty pieces supplied by the brands in each of their consignments is zero or not. For this, the manager collects data from the two brands. Suppose that the mean number of faulty pieces supplied by the brands are independent of each other. Let n denote the number of consignments for which the data was collected, X denote the sample mean of the number of faulty pieces supplied per consignment by each brand, and S denote the sample standard deviation in the number of faulty pieces supplied per consignment by each brand. The given table shows the data collected. Brand n A 120 Χ 15.21 S 11.2 B 95 10.11 14.1 The manager's null hypothesis would be that the difference between the mean number of faulty pieces supplied per consignment by brands A and B is The manager's alternative hypothesis would be that the difference between the mean number of faulty pieces supplied per consignment by brands A and B is The standard error of the difference between the sample means is: (Round your answer to two decimal places.) The t-statistic for testing the null hypothesis is (Round your answer to two decimal places.) Given the value of the t-statistic, for a prespecified 1% level of significance, we the null hypothesis.