 # MATH 171 Fundamental Concept Of Mathematics

## Question:

The survey responses of students who took Math 171 courses in fall 2018 are contained in the data file.

The data are for students’ weight, separated by sex.

The data is for the weight of students, separated by sex. Tell me which sex you would like to use in this project.

Use the Excel file “Weights.xlsx”, reproduced at the end of the page, to create a simple random sample

Of 36 students.

A 2-3 page paper should be prepared in Times New Roman font, 12 with one inch margins.

Include a detailed explanation about how you selected your sample in the paper.

It should also explain why this study is experimental or observational, as well as the population.

The paper should provide a detailed explanation as to why or why this data should not be used to assume the Longwood student body, Virginia college students, and the overall United States population.

A summary should be included for both the numerical and graphic data.

If you use a calculator to calculate, then include the random number used as the fourth digit of the phone number of one member. Make sure you explain.

You should explain the line that you are using if you use a random digits table.

Random sampling simply involves picking units out to form a desired size sample. This ensures that each unit in the population has an equal chance of being chosen if it is possible.

In this case, we had a population representing the weight of male students that was 94 units. However, our desired size was 36. Therefore, the following steps were taken to sample 36 units out of a population representing the weight of male students.

Step 1

First, we needed to identify our population. There was a record of 94 male students at different weights.

Step 2

The second step is to decide the size of the sampling. We chose 36 students as the sample size.

Step 3

The third step is the following: After recording data on excel, click on data analysis at the top left corner. Next, select method of sampling. Click on the option under data. Select a random option. 36 students were selected to represent the sample size. On the option of output, click on the first excel cell under random sampling. Finally click on ok.

The term observation studies is the recording of patterns of behavior or events objects in a logical fashion in order gather sufficient information about an occurrence. (Mason 2010).

The key element that distinguishes observation studies from experimental studies, is the fact that it focuses only on the targeted behavior.

Two approaches can be used to conduct observation research. One is structured observation, where the researcher has prior knowledge about the research and is able to use that information to determine the recording method.

This is because the first observation approach is focused on reducing bias.

The unstructured observation approach, in which the problem has not been identified yet, raises the risk of the researcher being biased based on their judgments about the data.

The analysis included observational data. This meant that a group of 94 male students were asked about their weight. Every student answered by giving his response to whether he has ever measured himself. However, because the interviewers did not have control over the data, this data will be considered as association data.

Random sampling is the best option to determine the body weight of male and female Longwood students. It also works well for the Virginia college student population.

Random sampling in large populations helps to minimize the cost of analyzing the entire population. It also saves time and allows for a better understanding of the data.

The third reason is that it can be tedious when dealing with large numbers of people. Fourthly, larger populations make it more accessible to all, which will lead to higher biases.

Mean weight = Total Weight / Number of Variables

Variance =

Standard deviation = Square Root of Variance

Scatter diagram for the random sample

Conclusion

Conclusion: Random sampling can save you time, money and effort. When the sampling strategy is right, the size of the sample is carefully chosen and there is a chance of sampling error being reduced, then the result of the sample is valid and reliable.

It is evident that the scatter graph shows a positive relationship between random weight and male student numbers.

Confidence intervals

Confidence interval is the range between statics that approximates the true value of a population.

The 95% confidence interval is the range that 95% of the population is true to, while the 99%confidence interval (Lakens, 2013,) is the range that 99% of the population is true to.

Calculations that involve 99% intervals will have greater ranges than those that include 95%. However, if you are looking for the exact value, then a narrower range will provide a better sample size.

Calculating interval levels using a formula

Write down the occurrence to be tested.

Step 2

You can randomly select the data you need from a large population.

Step 3

Calculation of standard deviation and sample mean.

The chosen population can be used to determine the statistic sampling you will use to calculate the parameter, the standard deviation or the mean.

To calculate the sample mean, add all the samples units together to get the total. Divide it by the total number of samples.

First, you will need to calculate the mean. Then, you will need to determine the mean square differential, which can be categorized as a variance. The standard deviation will then have to be calculated by finding the square root.

Step 4

You can also choose the confidence level you want to use in the calculation. This ranges between 90%, 95% or 99%.

Step 5

Calculation of margin of error

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

The formula represents calculation which involves multiplying the standard deviation and critical value together.

First convert the confidence level in decimals from the percentage and then divide it by 2 to get Za/2. This is followed by checking the table z to find its equivalent. In this example, the 95% interval corresponds to 1.96.

The standard error can be calculated by taking the standard variance and then dividing it by the square root of sample size.

Next, multiply the corresponding values of z tables and the standard errors to calculate the marginal error.

Step 6

The last step involves stating confidence level. We take the mean add and subtract it with margin errors. This will allow us to determine the upper or lower level of the bounded level confidence level.

Calculations

Newton’s recorded weight was

The mean weight for male students = 181.0278N

1 N = 0.224809 pounds force

181.0278 N = 40.696668529 L pound force

= 40.7 pound force

Calculation of a confidence interval of 95%

Multiply 1.96 by standard deviation and divide it with sample size

The sample size is 36 students

95% interval will be used to determine the average weight for each student.

The 24.913-pound average weight will be the lowest, and 49.087 will be the highest.

The 95% confidence level allows us to conclude that the average weight for male students is between 24.913 and 40.087 pounds.

Determination a 99% confidence interval

Multiply 2.58 by the standard error and divide it with the sample size

The sample size is 36 students

99% interval for average weight of student will be equivalent

The 21.09-pound average weight will be the lowest, and 52.09 pounds will be its highest.

We can conclude that the average weight for male students is between 21.09lbs and 52.09lbs with the 99% confidence.

References

Participant observation.

Emerging trends within the social and behavioral sciences: A interdisciplinary, searchable and linkable resource. pp.1-15

A practical guide to t-tests, ANOVAs, and how to calculate and report effect sizes in order facilitate cumulative science.

Frontiers of psychology, 4, p.863.

Sample size and saturation in PhD research using qualitative interviews.

Montgomery, D.C. Runger G.C. 2010,

Probability and applied statistics are for engineers.

John Wiley & Sons.

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