PROBLEM 2 [TWO INDEPENDENT SAMPLES] [40 POINTS=10+10+10+10] BILL INTENDS TO COMPARE EFFICIENCY FOR TWO MORTGAGE LENDERS (BANK OF AMERICA AND CHASE) TO FIND OUT WHICH IS WORKING HARDER. HE USES THE SAME RECORDS AS ANN (OBTAINED FROM THE PREVIOUS PROBLEM) TO ANALYZE TIME SPENT BY 10 LOAN OFFICERS OF EACH BANK. THE INDIVIDUAL TIMES ARE ASSUMED TO BE NORMALLY DISTRIBUTED WITH UNKNOWN PARAMETERS. THE SAMPLE SUMMARIES ARE SHOWN IN THE TABLE BELOW. AVERAGE TIME FOR BANK OF AMERICA WAS 61.4 MINUTES PER CUSTOMER, WITH THE STANDARD DEVIATION 5 MINUTES. AVERAGE TIME FOR CHASE WAS 70.2 MINUTES, WITH THE STANDARD DEVIATION = 25 MINUTES. SIZE MEAN SAMPLE SUMMARIES SD N 10 (X-BAR), = 61.4 S=5 SOURCE BOA VARIANCE V=S/N (S)=25 25/10=2.5 CHASE N= 10 | (X-BAR);=70.2 | S=15 (S)2=225 225/10-22.5 BILL BELIEVES THAT THE POPULATION VARIANCES ARE ENTIRELY UNKNOWN. (D) HELP BOB TO ESTIMATE THE DIFFERENCE BETWEEN TWO POPULATION AVERAGE VALUES WITH 95% CONFIDENCE AND SHOW ALL NECESSARY ITEMS LISTED BELOW. CRITICAL VALUE= MID-POINT= MARGIN OF ERROR = UPPER CONFIDENCE LIMIT= LOWER CONFIDENCE LIMIT= WIDTH OF THE INTERVAL=