# Statistical Methods For Rates and Proportions

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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
1.9599
64
margin of
error
244.99
55
Upper limit
7744.9
95
Lower limit
7255.0
05
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
1.9599
64
margin of
error
195.99
64
Upper limit
7695.9
96
Lower limit
7304.0
04
Part (b)

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