perform data analysis by comparing students who were born outside the USA to students who were born in the USA on several measures. Specifically, you are going to answer the following research questions:
1. Do students who were born outside the USA have a higher mean GPA than students who were born in in the USA?
2. Do students who were born outside the USA spend more time on their homework than students who were born in the USA?
3. Do students who were born outside the USA have a higher mean age than students who were born in the USA?
In order to answer the research questions above, you will need to select a sample of students who were born in the USA, and a sample of students who were born outside the USA, and compare them on the selected measures. Please follow the instructions below to select your sample and then answer ALL of the questions which follow.
1. Go into D2L and open the folder named STUDENT SURVEY, then open the file named STUDENT SURVEY DATA FILE.
2. Using the random number generator http://stattrek.com/Tables/Random.aspx. Select a random sample of 30 students who were born in the USA and a random sample of 30 students who were born outside the USA using the variable “COB” (Country of Birth). The data file is already sorted by country of birth. Students born outside the USA are listed from # 1 through #171. Students born in the USA are listed from #172 through #435. You can also select your sample by using a systematic random sample but you must clearly specify the method you used. For example, every 5th student, or every 10th student, etc.
Indicate which sampling method you used and list the student id number of those selected in the samples as well as the values for the variables you will analyze.
3. For each student selected in your samples, list the values for each of the following variables:
a. Age
b. GPA
c. Hours spent on school work at home
Your final data file will look like this: (SEE BELOW)
STUDENT ID AGE GPA HRS SPENT ON SCHOOL WORK AT HOME
4. Using the variable Age, construct TWO frequency distributions to summarize the Ages of students born in the USA and those born outside the USA. Use 5 classes to construct your frequency distribution. For each frequency distribution, show your calculations for the class width and then list the:
a. Lower limits and upper limits
b. Class boundaries
c. Class mid-points
d. Relative frequencies
e. Cumulative frequencies
5. Using the variable hours spent on school work at home, construct TWO frequency distributions to summarize the hours of students born in the USA and those born outside the USA. Use 5 classes to construct your frequency distribution. For each frequency distribution, show your calculations for the class width and then list the:
a. Lower limits and upper limits
b. Class boundaries
c. Class mid-points
d. Relative frequencies
e. Cumulative frequencies
6. Using Excel create four histograms, properly labeled, depicting the data from the frequency distributions in # 4 and #5above.
7. Describe the shape of the data for each frequency distribution. Is it normally distributed? Positively skewed, negatively skewed, uniform? Or maybe it cannot be clearly determined from your sample data, in which case you would indicate “shape cannot be determined”.
8. Make one observation about each of the frequency distributions or histograms you have constructed? For example, with the “ages” of students, you could say that “xx percent of students born in the USA are less than xx years old. Or you could say that “xx percent of students born outside the USA are between xx and xx years old”.
9. For your sample of students born in the USA and for your sample of students born outside the USA, list the values for the variables GPA and hours spent on school work at home and then compute the following for each variable:
a. mean
b. median
c. mode
d. mid-range
e. range
f. standard deviation
g. variance
h. Q1, Q2, and Q3
i. 90th percentile
j. Identify any outliers
10. Construct a 5-number summary and boxplot using the variable “hours spent on school work at home” for both groups.
11. Compare the means for both groups to answer the research questions in the first paragraph. Which group has a higher mean GPA? Which group spends more time on their homework? What conclusions can you draw about students who were born in the USA and those who were born outside the USA based on this analysis?
