The data file for this project contains the survey answers from students registered for Math 171 courses in fall 2018. The data is for the weight of students, separated by sex. You should choose one sex to use in this project – tell me which one. Using the Excel file “Weights.xlsx”, which is reproduced on the last page, create a simple random sample

of 36 students. Write a 2-3 page paper in Times New Roman font size 12 with one inch margins and double spaced. The paper should include a detailed explanation of how you determined your sample.

The paper should also include an explanation of why this study is considered observational or experimental as well as the population of the study. The paper should include a detailed explanation of why or why not this data should be used to make assumptions of the entire Longwood student population, the Virginia college student population, and the general United States population. Finally, the paper should contain a summary, both graphical and numerical, for the sample data.

If you use a calculator, then you should include the random seed used as the last four digits of one member’s phone number – be sure to explain. If you use a table of random digits, be sure to explain which line to start with.

## Simple Random Sampling

A simple random sampling involves selecting out units to form a desired sample size, in which each unit on this population will have an equal probability of being selected if possible. In our case we had a population of 94 units representing weight of the male students, but our desired size was 36 units, therefore the following were the steps used in sampling out 36 units from a population of 94 units that were representing weight of the male students;

Step 1

The first thing was to define our population, where we had a record of 94 male students with different weights.

Step 2

The second step is to choose the size of the sampling, where the sample size was taken to be 36 students

Step 3

The third step will involve the following procedure on the excel sheet; after recording the data on the excel, on the tool bar of excel the option of data was click and data analysis was clicked at the data tab on the top right corner, an option of sampling was picked, a data input range was select which included all the weights of the 94 male students, under method of sampling a random option is click and 36 number of students is written to represent sample size needed, on the option of output the first cell on the excel sheet under random sampling is clicked and finally an ok is clicked at a 36 random students with their weights is selected from a population of 94 students.

Observation studies can defined as a record of pattern of behaviors of people or events object in logical manner in order to gather enough information about an occurrence (Mason, 2010). The key factor that differentiates the observation from experimental studies is through concentrating only in observing the targeted behavior.

The research done through observation techniques comprises of two approaches, which includes structured and unstructured (Jorgensen, 2015 ) , where in structured observation it elaborates the prior knowledge of the research precipitation on his analysis where the data to be observed is already known and the method the researcher will use in recording is also known.

The important of this first approach of observation is banked on reducing any biasness that may be subjected by the researcher and emphasizes on consistence of the data, its suitability is only based on the problem being known and its responses can be seen clearly. Contrary to this is the approach of unstructured observation where the problem if not yet defined, the possibility of the researcher being bias is also higher on his or her judgments on the data observed.

## Observational Study vs. Experimental Study

The studies involved in this analysis was observational, where a population of 94 male students were interviewed regarding their weight and every student was giving out his respond in regard to what he had one time measured, it was proved by any procedural experiment to ascertain that their response were accurate, the interviewers only concentrated on recording the responses of the students, therefore they lack the control over the data and will only be regarded as association data.

Random sampling is the best method that will be used to determine the weight of male student or female students in Longwood student population, the Virginia college student population, and the general United States population. The reason behind having a random sample in large population is to minimize the cost that will incurred if the whole population will be considered, it also saves on time on getting to understand the large data what actually it portrays. Thirdly, it also tiresome if dealing with large population, fourthly, dealing with larger population makes it partially accessible to the whole group and this will have higher chances of biasness.the whole population from appendix

Mean weight = Total weight / number of variables

= 6517/36

= 181.0278

Variance =

= 45620.97/36-1

= 1303.456

Standard deviation = square root of variance

= Sqrt(1303.456)

= 36.10341

Scatter diagram of the random sample

Conclusion

In conclusion, the use of random sampling method will mainly save on time and money, and the best strategy of sampling is chosen, and the selection of sampling size is done appropriately, and caution is taken in a reduction of sampling error, then the outcome of the sample will be valid and the information will be totally reliable.

From the scatter graph, there is a positive relationship between the random weight of the male students and the number of the male students.

Confidence intervals

The term confidence interval is defined as the range that approximates where a true value of a population will lie between in statics (Montgomery and Runger, 2010). Therefore 95%confidence interval is defined as the range that is 95% certain it contains a true value of a population, while 99%confidence interval is defined as the range that is 99% certain it contains a true value of a population (Lakens, 2013).

Calculation that involves 99% intervals will have a wider range as compared to 95% which will be shorter, from this scenario it is clear that the calculation that will result to a wide range is more likely to be accurate to contain the true value as compared to a shorter range, this means there that 99% is accurate it will contain the true value, but if one is seeking for a precise value then a narrow range having a higher sample size as determined using 95% will result to it.

## Use of Data to Make Assumptions of Different Populations

Procedure for calculating interval levels

Step1

Write down the occurrence that is supposed to be tested, this means that write out the average sample that is supposed to be accurately to be predicted.

Step 2

Sample randomly the data that you want to use from a a large sample population

Step 3

Calculation of sample mean and standard deviation..

Using the chosen population decide on the parameter using statistic sample you want to calculate, either the standard deviation or mean.

Sample mean is calculate by adding all the samples units to get the total and divide it with the total number of units, this can be represent as x- bar = total samples/number of the samples

Standard deviation is determined by first calculating the mean, this will be followed by determining the mean square difference, which can be classified as a variance, and the standard deviation will then be determined by finding the square root of the variance.

Step 4

Choosing the desired confidence level, which ranges from 90%, 95% and 99%, this may also be provided in order to be used in the calculation.

Step 5

Calculation of the margin of error

This will be determined by the following formula

Confidence coefficient = Z_{a/2} * * Z_{a/2}

Where, a = level of confidence, is deviation standard, n is the sample size

The formula represents calculation that involves multiplying both the standard deviation and critical values together.

- Finding critical value you first convert the confidence level into decimals from the percentage, then divide it by two to represent Z
_{a/2}, this if followed by checking the table of z to find the value that corresponds to it, for example for 95% interval the corresponding value from the z table will be 1.96. - The standard error is determined by taking the standard deviation and then dividing it with the square root of the sample size.
- Then multiplication of the corresponding value of z table and the standard error follows, in order to determine the marginal error.

Step 6

The final steps involves stating the confidence level, where we take the mean add to subtract it with margin error, this will help in determining the upper or higher level and lower levels of the bounded confidence level.

**Calculations **

The weight recorded were in Newton’s

The mean weight of the male student = 181.0278 N

1 N = 0.224809 pound force

181.0278 N = 40.696668529 pound force

= 40.7 pound force

Determination of a 95% confidence interval

Mean = 40.7 pound

s.d = 37 pounds

Multiplying 1.96 by the standard deviation and dividing it with the sample size

The sample size = 36 students

= 1.96 * 37/sqrt(36)

= 12.087

95% interval for the average weight of the student will be equivalent to

37 pounds

The lower average weight will be 24.913 pounds while the higher average weight will be 49.087 pounds

With the 95% confidence, we can conclude that the average weight of the male students is between 24.913 pounds and 49.087 pounds.

**Determination of a 99% confidence interval**

Mean = 40.7 pound

s.d = 37 pounds

Multiplying 2.58 by the standard deviation and dividing it with the sample size

The sample size = 36 students

= 2.58 * 37/sqrt(36)

= 15.91

99% interval for the average weight of the student will be equivalent to

37 pounds

The lower average weight will be 21.09 pounds while the higher average weight will be 52.09 pounds

With the 99% confidence, we can conclude that the average weight of the male students is between 21.09 pounds and 52.09 pounds.

References

Jorgensen, D.L., 2015. Participant observation. Emerging trends in the social and behavioral sciences: An interdisciplinary, searchable, and linkable resource, pp.1-15.

Lakens, D., 2013. Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Frontiers in psychology, 4, p.863.

Mason, M., 2010, August. Sample size and saturation in PhD studies using qualitative interviews. In Forum qualitative Sozialforschung/Forum: qualitative social research (Vol. 11, No. 3).

Montgomery, D.C. and Runger, G.C., 2010. Applied statistics and probability for engineers. John Wiley & Sons.

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