Data Analysis Assignment Solution: Statistics Module, Semester 1

This document presents a complete solution to a data analysis assignment, addressing key statistical concepts. The solution includes detailed calculations, interpretations, and explanations for each problem. The assignment covers topics such as confidence intervals, the Central Limit Theorem, and the application of statistical methods to real-world scenarios. The solution includes the correct assumptions, calculations, and interpretations of the results. The assignment also includes the use of z-values, sample size determination, and the analysis of proportions. The document is designed to help students understand and apply statistical principles effectively, providing a valuable resource for academic success. The solution also discusses the limitations of the analysis and the implications of the findings.

Running head: DATA ANALYSIS 1
Data Analysis
by
Student’s Name
Name of Institution

DATA ANALYSIS 2
8.23
a).
Column1 Mean 1.7234
95% C.I 0.033439
Mean 1.7234
Standard Error 0.01635
Median 1.735 Lower limit 1.689961
Mode 1.662 Upper Limit 1.756839
Standard Deviation 0.089551
Sample Variance 0.008019
Kurtosis -0.24355
Skewness -0.36714
Range 0.348
Minimum 1.522
Maximum 1.87
Sum 51.702
Count 30
Confidence Level(95.0%) 0.033439
b) The assumption made is that the data follows a normal distribution, otherwise, n being 30 is
large enough for the Central Limit Theorem to be applied (Fischer, 2010).
c) The assumption is valid because the distribution of a sample requires a normal distribution for
a confidence interval to be constructed. The Central Limit Theorem states that if you take a large
sample with replacement from a population with mean, μ and standard deviation, σ , the sample
mean will follow approximately a normal distribution (Rotondi, 2012).

DATA ANALYSIS 3
8.10
a)
mean 7500
standard
deviation 1000
sample size 64
alpha 0.05
z value
1.95996
4
margin of error
244.995
5
Upper limit
7744.99
5
Lower limit
7255.00
5
b) The manufacturer has no right to state that the compact fluorescent bulbs have a mean life of
8000 hours because at 95% confidence level the upper limit is 7745 hours.
c) Yes, the assumption must be true in order to apply the Central Limit Theorem in finding
confidence intervals.
d) Part (a)
mean 7500
standard
deviation 800
sample size 64
alpha 0.05
z value
1.95996
4
margin of error
195.996
4
Upper limit
7695.99
6
Lower limit
7304.00
4

DATA ANALYSIS 4
Part (b)
Still the manufacturer has no right to state a mean of 8000 hours since the new higher limit is
7696 hours.
8.32 a)
Alpha 0.05
Proportion
0.87057
7
Sample size 1074
q
0.12942
3
z value
1.95996
4
margin of error
0.02007
5
Lower limit of
CI
0.85050
2
Upper limit of
CI
0.89065
2
b)
Alpha 0.05
Proportion 0.39013
Sample size 1074
q 0.60987
z value
1.95996
4
margin of error
0.02917
2
Lower limit of
CI
0.36095
8
Upper limit of
CI
0.41930
3

DATA ANALYSIS 5
c) Many Facebook users are connected to friends in the past than to people they have never met
in person.

DATA ANALYSIS 6
Works Cited
Fischer, H. (2010). A history of the central limit theorem: From classical to modern probability
theory. Springer Science & Business Media.
Fleiss, J. L. (2013). Statistical methods for rates and proportions. John Wiley $ Sons.
Greenland, S. S. (2016). Statistical tests, P values, confidence intervals, and power: a guide to
misinterpretations. European journal of epidemiology, 337-350.
Rotondi, M. A. (2012). A confidence interval approach to sample size estimation for
interobserver agreement studies with multiple raters and outcomes. Journal of clinical
epidemiology, 778-784.