BUSS 305 STATISTICAL DECISION MAKING.

UNIVERSITY EXAMINATIONS: 2021/2022
EXAMINATION FOR DEGREE OF BACHELOR OF BUSINESS AND
INFROMATION TECHNOLOGY
BUSS 305: STATISTICAL DECISION MAKING
DATE: DECEMBER, 2021 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any Other Two Questions

QUESTION ONE (20 Marks)
(a) A study involves selecting a random sample of 300 sales representatives. One item of
interest is their annual income. The sample mean is Sh. 55,420 and the sample standard
deviation is Sh. 2,050.
i. What is the point estimate? (2 Marks)
ii. Determine the standard error of the mean. (2 Marks)
iii. What is the 90% confidence interval for the population mean rounded to the
nearest
Sh. 10? (3 Marks)
iv. What would be the effect of increasing the sample size on the confidence interval
in (iii) above? (1 Mark)
Suppose that you wish to predict the income of university cafeterias on the basis of floor space
and number of employees. A sample of 5 cafeterias give the following data.

i) Calculate the estimated regression equation. (10 Marks)
ii) Estimate the income when the floor space is 12,000 square feet and 11 employees.
(2 Marks)
QUESTION TWO (15 Marks)
a) Write brief notes on the following sampling methods giving examples
i. Snowball sampling [3 Marks]
ii. Cluster sampling [3 Marks]
(b)A construction firm has placed an order that they require a consignment of wires which have a
mean length of 10.5 meters with a standard deviation of 1.7m. the company which produces the
wires delivered 90 wires, which had a mean length of 9.2m. The construction company rejected
the consignment on the grounds that they were different from the order placed. Conduct a
statistical test to indicate whether you support the action taken by the construction company at
5% level of significance. [6 Marks]
(c) In what circumstances is a significance test based on the t-distribution used in preference to a
significance test based on the normal distribution? (3 Marks)
QUESTION THREE (15 Marks)
a.) What is the purpose of estimation? [2 Marks]
b.) Memory capacity of 9 students was tested before and after training. State whether training
was effective or not from the following scores: Use α = 0.01

(6 Marks)
(c) From the adult population of four large cities, random sample of sizes given below were
taken and the number of married and single men recorded. Do the data indicate any significant
variation among the cities in the tendency of men to marry? Test at 5% significance level.

(7 Marks)
QUESTION FOUR (15 Marks)
(a)In county A with 300 people, 56% people preferred using small size computers while in
country L with 200 people 48% preferred using small size computers. Test whether there is a
difference between the proportions in district L and K at 5% of significance.
(6 Marks)
(b) State three limitations of decision tree approach. (3 Marks)
(c)A client asks estate agent to sell three properties A, B and C for him and agrees to pay 5%
commission on each sale. He specifies certain conditions. The estate must sell property A first,
and this he must do within 60 days. If and when agent receives his 5% commission on that sale.
He can either back out at this stage or nominate and try to sell one of the remaining two
properties within 60 days. If he does not succeed in selling the nominated property in that period,
he is not given the opportunity to sell the other. If he does sell it in the period, he is given the
opportunity to sell the third property on the same conditions. The following table summarizes the
prices, selling cost (incurred by the estate agent whenever a sale is made) and the estate agent’s
estimated probability of making a sale.

i) Draw up an appropriate decision tree for the estate agent. (3 Marks)
ii) What is the estate agent’s best strategy under EMV (Expected Monetary Value)
approach?
(3 Marks)

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