How many 11 letter words can be formed by rearranging the letters of the word CORONAVIRUS?

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

 

QUESTION ONE

(a)    How many 11 letter words can be formed by rearranging the letters of the word CORONAVIRUS?  [5 Marks]

(b)   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]

(c)    Briefly describe the three branches of statistics.    [5 Marks]                                                            

QUESTION TWO

 (a)    Give two limitations of a Chi-square test.       [2 Marks]

(b)   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:

At the 5% level of significance, is income independent of the level of satisfaction derived from the use of public parks.    [13 Marks]

(c)    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.  [10 Marks]

 QUESTION THREE

(a)    The administration of an inner-city college has generally assumed that the average age of a student is no more than 20 years. The standard deviation of the age of students is known to be 3.6 from previous data. However, lately the students have appeared to be older than before, and some administrators say that the average age could be higher than 20 years. You collect a random age sample of 50 students and calculate a mean of 20.76. At the 90% level of confidence, can you conclude that the average age of students has indeed increased?       [10 Marks]

 (b)   Describe briefly two purposive sampling techniques with their uses and limitations. [5 Marks]

(c)    Football fans of both Dockers and Eagles were asked their opinion of the quality of the facilities at the Subiaco Oval. The following table cross-classifies the information provided by the fans.

At the 99% level of confidence is there a relationship between the opinion of the quality of the oval and the club the fan supports?     [10Marks]                                                                                                                                                                       

  

QUESTION FOUR

(a)    Give five advantages of a completely randomized design, CRD.           [5 Marks]

 (b)   Suppose you are interested in developing a counselling technique to reduce stress within marriages. You randomly select two samples of married individuals out of ten churches in the association. You provide Group 1 with group counselling and study materials. You provide Group 2 with individual counselling and study materials. At the conclusion of the treatment period, you measure the level of marital stress in the group members. Here are the scores:  

Are these groups significantly different in marital stress? Test at 5% level of significance.       [10 Marks]

(c)    A manufacturer claims that the average weight of a tin of baked beans is 440 g and the standard deviation is known to be 20 g.  From a random sample of 100 cans you calculate the average weight to be 435 g.  At the 95% level of confidence, is there a change in the average weight of a can of baked beans?   [10 Marks]

 

QUESTION FIVE

(a)    A machine which fills orange squash bottles should be set to deliver 725 ml. A sample of 50 bottles is checked and the mean quantity is found to be 721 ml and the sample s.d. is 13 ml. Does this differ significantly from 725 ml at the 1% level? Find the probability of Type I error for this test.      [10 Marks]

 (b)   Prove the formula  [5 Marks]

 (c)    A random sample of 10 hot drinks from Dispenser A had a mean volume of 203ml and a standard deviation of 3ml. A random sample of 15 hot drinks from Dispenser B gave corresponding values of 206ml and 5ml. The amount dispensed by each machine maybe assumed to be normally distributed. Test at the 5% significance level, the hypothesis that there is no difference in the variability of the volume dispensed by the two machines.

 

 

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