QUESTION ONE How many 11 letter words can be formed by rearranging the letters of the word CORONAVIRUS? [5 Marks] A supermarket chain conducted a study to determine where to place its generic-brand products in order to increase sales. Sales (in thousands of Kwacha) for one week were as follows:

Shop A Shop B Shop C

High Shelf 60 55 50

Eye-level shelf 55 60 58

Low shelf 57 57 56

Using the level of significance, do the shelves differ significantly in attracting customers to buy these generic brand products? [15 Marks] Briefly describe the three branches of statistics. [5 Marks]

QUESTION TWO

Give two limitations of a Chi-square test. [2 Marks] A tourism student wishes to find out if level of satisfaction a person derives from the use of public parks is related to the income of that person. From administering 400 questionnaires, the following information was obtained:

Level of Satisfaction

Above Average Average Below Average

High income 20 10 10

Middle income 30 50 80

Low income 10 60 130

At the 5% level of significance, is income independent of the level of satisfaction derived from the use of public parks. [13 Marks] Let the population be given by the numbers. Take all random samples of size 3 without replacement and obtain the sampling distribution of the sample mean.