**UNIVERSITY EXAMINATIONS: 2018/2019**

**EXAMINATION FOR THE DEGREE OF MASTERS OF SCIENCE IN **

**DATA ANALYTICS**

**MDA5201 MATHEMATICAL STATISTICS AND DATA ANALYSIS**

**PART-TIME/ WEEKEND**

**DATE: DECEMBER, 2018 TIME: 2 HOURS**

**INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.**

**QUESTION ONE: (20 MARKS)**

a) Define each of the following statistical terms/concepts

i. Significance level [2 Marks]

ii. Statistical power [2 Marks]

iii. Parameter [2 Marks]

iv. Random assignment [2 Marks]

v. Effect size [2 Marks]

b) Suppose X is uniformly distributed in the range 0 to 1. What is the mean of X?

[2 Marks]

c) Suppose that x is a binomial random variable with n = 5 and p = 0.5.

i. For each value of x, calculate p(x) and construct a probability distribution table

for this phenomenon. [2 Marks]

ii. Sketch an histogram for this distribution [2 Marks]

iii. Find

[2 Marks]

iv. Find the expected value of x [2 Marks]

**QUESTION TWO: (15 MARKS)**

Suppose scores on the 2018 KCPE examinations were known to be normally distributed with

mean 300 and variance 3600. For a survey of standard 8th leavers in the country, a random

sample of size 900 is selected. Find,

(a) The standard deviation (otherwise known as standard error) of the mean KCPE score

originating from this sample. [4 Marks]

(b) The probability that the mean KCPE score from this sample will (i) fall between 280 and

305 (ii) be greater than 304. [6 Marks]

(c) Find the number of additional subjects needed to double the precision of this estimate.

[5 Marks]

**QUESTION THREE: (15 MARKS)**

In a study to assess the impact of mobility on standard seven students’ mathematics achievement, the

following descriptive statistics were obtained from SPSS:

Descriptive Statistics

Dependent Variable: Mathematics Score

State the null hypothesis for the study [2 Marks]

b. Name one statistical analytic technique you can use to test the hypothesis in (a) above

[4 Marks]

c. Test the hypothesis in (a) at the 0.05 level of significance. Include the critical value, the

observed test statistic, the decision rule, and your decision. [5 Marks]

d. In a sentence or two, write the interpretation of the findings in (c) [4 Marks]

**QUESTION FOUR: (15 MARKS)**

a. The correlation matrix below represents the relationship in the investment returns among

four portfolios (A, B, C, and D).

Describe the relationship among the four portfolios. [2 Marks]

ii. Suppose an investor intends to diversify his/her investment for optimum stability.

In which two portfolios can he/she invest to achieve this objective? Why?

[3 Marks]

b. Using the data below,

i. Sketch a scatterplot for the relationship between X and Y. [3 Marks]

ii. Describe the relationship between X and Y. [3 Marks]

iii. Compute the covariance of X and Y. [4 Marks]