MTH/218 Version 2 / 2
Student GPA Scenarios
Your team has been hired by a polling company to analyze student achievement at various universities. The polling company wants to know the average GPA of students; however, each university charges $5,000 for the data on all of their students.Is there another way to obtain the mean GPA of the students without asking the University for the data? Your ultimate task is to decide whether it is more cost effective and efficient to poll students or buy the data.
Sample data: http://media.pearsoncmg.com/aw/aw_weiss_elemstatistics_9/cw/focus_database/FocusSample.xls
Population data: http://media.pearsoncmg.com/aw/aw_weiss_elemstatistics_9/cw/focus_database/Focus.xls
There are three main roles in this scenario. Select a role and complete the task listed under the role.
Role #2 Guestimator
Before your company sends anyone out to collect samples, they need to know how the data will be collected.Your job is to consult the pollsters on how best to take their polls and to tell the company how confident they can be regarding the results.
a. Create a strategy for obtaining GPAs from students that would be random and would minimize bias.
b. The male and female pollsters have collected the sample data.Use their data from the focus group sample to calculate the mean and standard deviation of all the students sampled.
c. Create and interpret a 95% confidence interval for your sample data. Compare your mean and standard deviation to that of the population (if you completed the Statistics I course at UOPX, refer back to the Travel Risk Scenario from Week 4). Are you still 95% confident?
d. Your boss wants you to start preparing a plan for another poll. Calculate the minimum number of students that need to be polled to get a margin of error less than 0.2 GPA.
Role #2 Male Student Pollster
To test the idea of polling students to calculate the average GPA, you send a pollster to the campus of The University of Wisconsin - Eau Claire (UWEC). The pollster stands in the middle of campus and randomly asks male students what their age and GPA are.Use the sample data from the Weiss site (see link above) that shows the data the pollster collected. Sort it by sex to isolate the male students, then sort by age.
a. Do you think there would be any bias in the sampling technique, the questions asked, or the results? Explain.
b. Assuming that each day the pollster only sampled 1 age group, calculate the mean and standard deviation of each sample (each age group, i.e., all the 18 year olds, all the 19 year olds, etc.).
c. Create a histogram of the sample means to visualize the sample distribution of the sample means. Does it look like a normal curve? Explain.
d. Compare your sample means, standard deviations, and histogram to the mean, standard deviation and histogram from the population (if you completed the Statistics I course at UOPX, refer back to the Travel Risk Scenario from Week 4). What did you expect the sample means to be? Support your answer with a calculation using the population data. Discuss the sample error.
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Role #3 Female Student Pollster
To test the idea of polling students to calculate average GPA, you send a pollster to the campus of The University of Wisconsin - Eau Claire (UWEC). The pollster stands next to the library and asks female students what their age and GPA are. Use the sample data from the Weiss site (see link on first page) that shows the data that the pollster collected. Sort it by sex to isolate the female students, then sort by age.
a. Do you think there would be any bias in the sampling technique, the questions asked, or the results? Explain.
b. Assuming that each day the pollster only sampled 1 age group, calculate the mean and standard deviation of each sample (each age group, (i.e., all the 18 year olds, all the 19 year olds, etc.).
c. Create a histogram of the sample means to visualize the sample distribution of the sample means.Does it look like a normal curve? Explain.
d. Compare your sample means, standard deviations, and histogram to the mean, standard deviation and histogram from the population (if you completed the Statistics I course at UOPX, refer back to the Travel Risk Scenario from Week 4). What did you expect the sample means to be? Support your answer with a calculation using the population data. Discuss the sample error.
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