Manager of Shop C would like to estimate the average amount of expenditure by members in the last quarter. A random sample of 9 members are selected from the population of 5000 members using SRSWOR and their amount of expenditure ($) were as follow: 3350, 3280, 5200, 4300, 4000, 4100, 4530, 4250, 3971 (a) Estimate the mean amount of expenditure in the last quarter among all members and find its standard error. Correct your answers to 2 decimal places. (6 marks) (b) If the manager would like the point estimate of the mean expenditure among all members has error not more than $100 with 95% confidence, how many members to be selected? (4 marks) (c) Classification of members is introduced recently and will be updated at the beginning of every quarter. If a member spent at least $4000 in the last quarter, the membership classification will be upgraded from ordinary' to 'Silver' at the beginning of coming quarter. Estimate the proportion of members will be upgraded from ordinary' to 'Silver and calculate its standard error. Correct your answers to 4 decimal places. (6 marks) (d) Similar study will be conducted in the next quarter. Determine the (conservative) number of members to be chosen, if the error of the point estimate of the proportion of members will spend at least $4000 in the next quarter is not more than 0.1 at 95% level of confidence. Manager of Shop C would like to estimate the average amount of expenditure by members in the last quarter. A random sample of 9 members are selected from the population of 5000 members using SRSWOR and their amount of expenditure ($) were as follow: 3350, 3280, 5200, 4300, 4000, 4100, 4530, 4250, 3971 (a) Estimate the mean amount of expenditure in the last quarter among all members and find its standard error. Correct your answers to 2 decimal places. (6 marks) (b) If the manager would like the point estimate of the mean expenditure among all members has error not more than $100 with 95% confidence, how many members to be selected? (4 marks) (c) Classification of members is introduced recently and will be updated at the beginning of every quarter. If a member spent at least $4000 in the last quarter, the membership classification will be upgraded from ordinary' to 'Silver' at the beginning of coming quarter. Estimate the proportion of members will be upgraded from ordinary' to 'Silver and calculate its standard error. Correct your answers to 4 decimal places. (6 marks) (d) Similar study will be conducted in the next quarter. Determine the (conservative) number of members to be chosen, if the error of the point estimate of the proportion of members will spend at least $4000 in the next quarter is not more than 0.1 at 95% level of confidence
