a.Three machines in a workshop are equally efficient. To measure the efficiency of four operators the data on the number of units produced per shift b y each operator on different machines as follows; perform a hypothesis test at 5% level of significance weather the machine operators are equally efficient.

O erator I O erator Il O erator I ll O erator IV

22 24 27 23

20 19 23 24

19 17 21 18

b. The following table gives the average prices for certain food items at Kismayu port and the average amount of each item recommended as necessary to sustain a family of four in 1998. Find the Laspeyres and Paasches index to measure the amount of change of the 1998 prices on these items from 1998 to 2008.

item 1998 Price 2008 Price 1998 quantity 2008 Price

Sugar 10 30 25 30

Wheat - 23 60 55

butter 71 189 50 56

Sirloin S 91 359 25 32

Ground B 39 139 120 156

chicken 51 109 4 6