**MAASAI MARA UNIVERSITY**

**REGULAR UNIVERSITY EXAMINATIONS**

**2018/2019 ACADEMIC YEAR**

**FOURTH YEAR FIRST SEMESTER**

**SCHOOL OF BUSINESS AND ECONOMICS**

**BACHELOR OF SCIENCE IN ECONOMICS**

**AND STATISTICS**

**COURSE CODE: ECS 4103**

**COURSE TITLE: APPLIED STATISTICS**

**DATE: 10TH DECEMBER 2018 TIME: 0830 – 1030 HOURS **

**INSTRUCTIONS TO CANDIDATES**

**Answer Question ONE and any other THREE questions**

**This paper consists of TWO printed pages. Please turn over.**

**ECS 4103 – Applied Statistics**

**Question One**

(a) Explain the significance of statistics in production (6marks)

(b) Consider the data below which shows the quantity of sugar in millions of

tones (Y) per year and the value of out of dollars per ton, (X)

i. Using this data estimate the regression equation of Y on X (7marks)

ii. Test the hypothesis that the regression coefficient is significant at 5%

level (7marks)

iii. What percentage of the variation in Y is explained by variation in X

(5marks)

**Question Two**

From the sample below:

a) Calculate the variance of the estimates (8marks)

b) Test the significance of b1 and b2 at 5% level of significance. (7marks)

**Question Three**

(a) Given a sample with a mean µ = 100 and variance δ = 81, and a random

sample of n = 25 is obtained. What is the probability that the sample mean lies

between 98 and 101? (5marks)

(b) Given a population with a mean of 400 and a variance of 16. If a sample of

35 is obtained,

ECS 4103 – Applied Statistics

i. What is the probability that sample mean will be more than 412.

(5marks)

ii. What is the probability that sample mean will be less than or equal to

389 (5marks)

**Question Four**

The table below gives real per capita income in thousands of dollars Y with

the percentage of labour force in agriculture X1 and average years of schooling

of the population over 25 years of age X2 for 10 developed countries in 2018.

n 1 2 3 4 5 6 7 8 9 10

Y 6 8 8 7 7 12 9 8 9 10

X1 9 10 8 7 10 4 5 5 6 8

X2 8 13 11 10 12 16 10 10 12 14

a) Find the partial correlation coefficient between Y and X1 (7marks)

b) Find the partial correlation coefficient between Y and X2 (7marks)

c) Which of the two exogenous variables contribute more to the

explanatory power of the model? (1mark)

**Question Five**

(a) A researcher wishes to estimate the mean weekly wage of the several

thousands of workers employed in a firm within plus or minus Sh 20 and with

a 99% degree of confidence. From past experience, the researcher knows that

the weekly wages of these workers are normally distributed with a standard

deviation of Sh 40. What is the minimum sample size required. (5marks)

(b) Given the following

Income 138 152 104 112 114 154 116 110 134 106 114 128

Expenditure 18 24 12 20 18 20 14 16 24 12 22 16

Calculate the income elasticity of expenditure (10marks)