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Mathematics & Economics
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Case 4 SLP Sampling

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Math 201 Basics Statistics   SLP 4

 

In this assignment, you will continue to collect data for another 5–10 days. Write a paper (1–3 pages) including all of the following content:

 

•Recalculate the mean, standard deviation, and variance.

•Is your mean increasing or decreasing?

•Explain the effects of the larger sample size in relation to your data.

•Do you think the current sample you have is enough to draw an accurate conclusion, or do you need a larger sample?

•What conclusions can you draw from comparing both sets of data?

 

Submit your paper at the end of Module 4.

 

SLP Assignment Expectations

Answer all questions posted in the instructions. Use information from the modular background readings and videos as well as any good-quality resource you can find. Cite all sources in APA style and include a reference list at the end of your paper.

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Case 4 SLP SAMPLING
Name
Course: Math 201 Basic Statistics
Instructor:
Date:
Recalculated mean, standard deviation, and variance [15 observations]
Day
Time
x-xÌ…
(x-xÌ…)^2
1
35
-2.4
5.76
2
38
0.6
0.3634911.6134.56432-5.429.165402.66.76637-0.40.167380.60.36834-3.411.569457.657.761031-6.440.9611402.66.7612380.60.361336-1.41.961435-2.45.761533-4.419.36Sum561321.6Mean37.4Population variance 4.63Population standard deviation , σ
21.44
Sample variance
22.97
Sample standard deviation, s
4.79
Data statistics for the last 5 observations
Population variance
5.84
Population standard deviation , σ
2.42
Sample variance
7.3
Sample standard deviation, s2.7
The sample standard deviation and variance has the denominator representing the number of observations minus one. This is because the sample is less than 30 observations, which is considered as the value that represents large sample sizes. On the other hand, the population standard deviation and variance use the number of observations as the denominators.
Sample standard deviations variances are represented as:
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Decreasing mean
The mean decreased marginally compared to the first data set, and there were smaller differences in the last five observations compared to the first data set. The mean in this case is 37.4 from the fifteen observations compared to 37.9 minutes for the initial observations, while for the additional five observations the mean is 36.4 minutes. Even though, there is no specific pattern that emerges for the fifteen observations, the recorded data set for the additional five observations was decreasing. Additionally, since the mean for the data set is the lowest this has affected the overall mean. Even though, some samples may have either high or lower values, there are no big divergences from the initial mean. In any case, samples drawn from the same population do not necessarily show the same characteristics, but most will likely cluster around the population mean (Healey, 2010).
Effects of a larger sample size
The larger size from 10 to 15 observations may only represen...
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