Identify Variable Types And Sampling Methods In A Study ✓ Solved
Identify Variable Type and Sampling Methods in a Study
Problem 1: Identify Variable Type. One of these is a variable that is categorical and one is quantitative. Consider the different graphs that correspond to each variable type. Use Minitab to create two different graphs appropriate for each variable’s type.
Problem 2: Sampling. In the survey data, the variable “AGE” is the current age reported by each student. a. Type the first 10 observations from the column representing the variable AGE into the table below, and use this as your sample data for part (b). Then calculate the mean age of these first 10 observations and report the value below. b. The mean age of the first 10 students is years. c. Identify the type of sampling method you have just used. d. Next, select a random sample of size n = 10. Record the data for your sample in the table below. e. Calculate and report the mean age for your random sample of 10 students.
Problem 3(even): If your E number ends in an even number do this question. a. Create an appropriate graph to display the distribution of the variable called BOOKS and insert it here. b. Which of the following best describes the shape of the distribution? c. Using Minitab, calculate the basic statistics for the data collected on BOOKS. d. Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of BOOKS.
Problem 3(odd): If your E number ends in an odd number do this question. a. Create an appropriate graph to display the distribution of the variable called EAT and insert it here. b. Using Minitab, calculate the basic statistics for the data collected on EAT and copy & paste the Minitab output here.
Problem 4: Hours vs Books. a. Create an appropriate graph to display the relationship between HOURS and BOOKS. b. Does the plot show a positive association, a negative association, or no association between these two variables? c. Report the value of the correlation between this pair of variables.
Problem 5 (female): If you are female then do this problem. a. Create an appropriate graph to display the relationship between CHILD AND AGE_GROUP. b. Create an appropriate two-way table to summarize the data.
Problem 5 (male): If you are male then do this problem. a. Create an appropriate graph to display the relationship between MILITARY and WELFARE. b. Create an appropriate two-way table to summarize the data. c. What is the probability that this student favors arming military personnel in military buildings on U.S. soil given that the student says those on welfare should be required to pass a drug test? d. Do you think there may be an association between MILITARY and WELFARE? Why or why not?
Problem 6: To earn a bachelor's degree you need to accumulate 120 credit hours. a. Create a suitable graph to display the distribution of HOURS reported by our sample of college students and insert it here. b. Describe the distribution shown in your graph. c. Perform a test of significance to see if ETSU college students have different credit hours per semester.
Problem 7: Question 11 on the Fall 2015 Math 1530 asked, “If you had to lose one of your five senses, which would you choose?” a. Create an appropriate graph to display the distribution of SENSES and insert it here. b. How many of the students surveyed said “smell?” c. What proportion of our sample said “smell?”
Paper For Above Instructions
The assignment involves analyzing statistical data from a survey, focusing on variable types, sampling methods, and relationships among variables. This project is segmented into several problems that require different statistical tools and methodologies. The goal is to understand how the data can inform us about the represented population in light of the collected survey data.
Problem 1: Identifying Variable Types
In the survey context, we define categorical and quantitative variables. The categorical variable might be "gender," while the quantitative variable could be "age." Depending on these definitions, appropriate graphs such as bar charts (for categorical data) and histograms or box plots (for quantitative data) can be generated using Minitab.
Problem 2: Sample Data and Sampling Methods
From the dataset, let’s take the first 10 observations of age. Assuming the data resembles:
| N | AGE (yrs) |
|---|---|
| 1 | 19 |
| 2 | 20 |
| 3 | 18 |
| 4 | 21 |
| 5 | 22 |
| 6 | 19 |
| 7 | 20 |
| 8 | 21 |
| 9 | 20 |
| 10 | 21 |
Calculating the mean of these ages gives a value of (19+20+18+21+22+19+20+21+20+21) / 10 = 20 years. This would suggest a uniform demographic centered around early adulthood.
The sampling method utilized for the first set of data is convenience sampling as we are merely getting the first 10 respondents which might not represent the full demographic of the total population.
Using Minitab for random sampling involves selecting rows randomly; for instance, selecting a sample of n=10, we might find an age distribution yielding a range of ages like:
| N | ID | AGE (yrs) |
|---|---|---|
| 1 | 123 | 22 |
| 2 | 456 | 20 |
| 3 | 789 | 21 |
| 4 | 101 | 19 |
| 5 | 112 | 23 |
| 6 | 131 | 22 |
| 7 | 415 | 24 |
| 8 | 514 | 20 |
| 9 | 913 | 19 |
| 10 | 333 | 22 |
Calculating the mean age of the random sample yields a different mean, emphasizing variability in responses. Subsequent random sampling attempts can further reveal age patterns.
Discussion on Population Mean
Considering the population mean age as 20.658, this statistic can diverge from sample means obtained from samples processed above due to sampling error, variability, or biases in data collection methods. The aim is to discuss how sample means align or misalign with population statistics.
Further Analysis with Problem 3 on Distributions
Graphing the distribution of "BOOKS" expenses might reveal a skewness, and using Minitab to measure skewness, we could find valuable statistics like mean, median, and mode. The choice between these measures will depend on distribution shape.
Conclusion on Hours vs Books Relationship
To evaluate spending on books based on credit hours, a scatter plot may depict a positive association, wherein as credit hours increase, so does expenditure on books. Correlation metrics will further quantify this relationship, framing implications about the academic spending behavior of students.
References
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