QUESTION 6: [20] a) A teller at a branch of a savings bank located in a certain community has averaged 300 transactions daily over the past year. A random sample of 20 days during this year indicates a mean of 304,4 transactions with a variance of 479,61 transactions? Assuming that the daily transactions are normally distributed, test at a 5% level of significance whether the population mean daily transactions has increased (8) b) Shoprite Stores analysed the value of purchases made on credit card by a random sample of 25 of their credit card customers. The sample mean was found to be R170, with a sample standard deviation of R22. i. Calculate the standard error of the mean. (3) 51 Page CBCB012 NOV EXAMINATION 2021 ii. Calculate a 95% confidence interval for the true mean value of credit card purchases by all their credit card customers. Give the upper and lower limits of this interval to one decimal place. (5) iii. A manager at one branch of Shoprite Stores in Mankweng claims that the mean value of credit card purchases at the branch is R185. Do you think that it is likely that the Mankweng branch has a mean value of credit card purchases greater than the true mean of credit card purchases? Explain with reference to the interval that you have calculated in part (1) QUESTION 6: [20] a) A teller at a branch of a savings bank located in a certain community has averaged 300 transactions daily over the past year. A random sample of 20 days during this year indicates a mean of 304,4 transactions with a variance of 479,61 transactions? Assuming that the daily transactions are normally distributed, test at a 5% level of significance whether the population mean daily transactions has increased (8) b) Shoprite Stores analysed the value of purchases made on credit card by a random sample of 25 of their credit card customers. The sample mean was found to be R170, with a sample standard deviation of R22. i. Calculate the standard error of the mean. (3) 51 Page CBCB012 NOV EXAMINATION 2021 ii. Calculate a 95% confidence interval for the true mean value of credit card purchases by all their credit card customers. Give the upper and lower limits of this interval to one decimal place. (5) iii. A manager at one branch of Shoprite Stores in Mankweng claims that the mean value of credit card purchases at the branch is R185. Do you think that it is likely that the Mankweng branch has a mean value of credit card purchases greater than the true mean of credit card purchases? Explain with reference to the interval that you have calculated in part (1)
