Statistics and Data Analysis | Questions-Answers

Running head: STATISTICS AND DATA ANALYSIS 1
Statistics and Data Analysis
Student Name
Professor’s Name
University Name
Date

STATISTICS AND DATA ANALYSIS 2
Business Statistics Sampling & Distribution
Question 1: Solution
The finite correction population correction factor is used in determining the standard
error of a sampling distribution when the sample size n is large relative to the population size (N)
(Polit, 2010). i.e. when the sample size is more than 5% of the population size (N)
Question 2: Solution
The conditions to be met are np ≥ 10 and n( p−1)≥ 10 hence,
np ≥ 10 ≈ ( 30 x 0.34 )=10.2≥ 10
n( p−1)≥ 10 ≈ (30 x 0.66 )=19.8 ≥ 10
The above conditions are satisfied. The range of sampling errors is given by the following
empirical formula for two standard deviations (Selvanathan & Keller, 2017).
Z∗
√ p ( 1− p )
n
1.96∗
√ 0.34 (1−0.34 )
30
Range of sampling error=± 0.17
Question 3: Solution

STATISTICS AND DATA ANALYSIS 3
The sampling distribution is less variable than the population distribution because the sample
means do not vary as much as the individual values in the population (Freund, 2014). For
example, we needed to determine a statistical parameter for the population we would have to use
individual outcomes which can take a wide range of values that could either be very extreme or
less extreme. On the other hand, if we needed to determine the same parameter using the sample,
we would use the values in the sample and even though the extreme value in the sample would
have an effect would be reduced by the other values in the sample. With an increase in sample
size the effect of a single extreme value would be made smaller due to the averaging with more
values (Fowler, 2009).
Question 4: Solution
Similarity
The only similarity between standard deviation and standard error is that they are used in
experimental studies to present the characteristics of sample data to give a description of
statistical analysis results (Hinton, 2014).
Differences
 Standard deviation is the measure of dispersion or spread of a set of values from
the mean while standard error is the measure of statistical exactness of an
estimate.
 Standard deviation is descriptive while standard error is inferential.
 Standard deviation is the square root of variance while standard error is the
standard deviation divided by the square root of the sample size.