MATH 216 COMPUTER ORIENTED APPROACH TO STATISTICS ASSIGNMENT ATHABASCA UNIVERSITY

MATH 216 COMPUTER ORIENTED
APPROACH TO STATISTICS
ASSIGNMENT ATHABASCA
UNIVERSITY

, Show your work for this component. Where relevant, keep all your middle work as well as your final answer to a
minimum of four decimals, unless otherwise stated. For any test of hypothesis questions, show all steps in detail
and provide a conclusion in terms of the context of the question.

Problem 1. Population data
A population consists of 5 units: X = 5, 7, 9, 11, and 13. All units are given equal probability of selection and a
sample of size 2 is selected with replacement. Use the Central Limit Theorem to answer part (e) below.
a. Compute the population mean (µ), population variance (σ2), and population standard deviation (σ).
[3 marks]
Σ x 45
• Population Mean: μ= = =9
N 5

x x-µ ( x−μ)2

5 -4 16

7 -2 4

9 0 0

11 2 4

13 4 16

Σ=40
2 Σ ( x−μ) 2 40
• Variance: σ= = =8
N 5

• Standard Deviation: σ=
√ Σ ( x−μ) 2
N = 5
√
40 = 2.8284


b. Graph a probability histogram of the population values. Title this graph: Population Distribution. What is
the shape of the histogram? [2 marks]




1