MDA 5201 MATHEMATICAL STATISTICS AND DATA ANALYSIS KCA Past Paper

UNIVERSITY EXAMINATIONS: 2016/2017
EXAMINATION FOR THE DEGREE OF MASTERS OF SCIENCE IN
DATA ANALYTICS
MDA 5201 MATHEMATICAL STATISTICS AND DATA ANALYSIS
ORDINARY EXAMINATIONS
DATE: AUGUST, 2017 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.

QUESTION ONE (20 MARKS)
a) Compare and contrast the following statistical concepts
i. Statistic and parameter (2 Marks)
ii. Ordinal and nominal variables (2 Marks)
iii. Uniform and normal distributions (2 Marks)
b) Define and give an example of a discrete probability distribution. (4 Marks)
c) A coin is tossed three times with the result being head (h) or tail (t) at each trial.
i. List all possible outcomes of this experiment. (6 Marks)
ii. Find the probability of at least two heads. (4 Marks)
QUESTION TWO (15 MARKS)
A national survey revealed that the percentage of listeners who would rate KTN on a scale of 1,
2, 3, 4, and 5 are 5, 10, 20, 25, and 40 percent respectively. Let X denote the KTN rating.
(a) Construct a probability distribution table for this phenomenon (3 Marks)
(b) Identify and briefly describe the general shape of this distribution (2 Marks)
(c) Find the following probabilities


(1 Mark)
(d) Expected value or mean of X (4 Marks)
(e) Variance and standard deviation of X (4 Marks)

QUESTION THREE: (15 MARKS)
Recent trends reveal that ten percent of all Acura MDX cars purchased develop engine problems
within one year. Suppose in a given week, 10 Acura MDX cars were purchased. Let X denote the
number of cars that develop engine problems within one year. Find,

(c) Expected value of X (4 Marks)
(d) Variance and standard deviation of X (5 Marks)
QUESTION FOUR: (15 MARKS)
In a study to compare the cost of land per acre (in ksh 1,000 units) between two suburban regions
of Nairobi revealed the following descriptive statistics:
Descriptive Statistics

State the statistical model for this analysis and indicate the statistical analysis situation where
it is most appropriate. (4 Marks)
c) State the null hypothesis for this analysis (2 Marks)
d) Test the null hypothesis you stated in (c) above at 0.05 level of significance. Include
the critical value, the observed test statistic, decision rule, and your decision. (5 Marks)
Formulae Sheet

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