Overview:
For this assignment, you will utilize statistical technology to work with a series of datasets. You are welcome to use the technology of your choice including Excel, Desmos, and Google Sheets. Please follow the instructions below. Once you have completed the assignment, submit your completed document (in .docx or .doc format) using the Submission Link.
Instructions:
- Download the file attached to this assignment. This file contains three questions.
- Copy and paste the graphs and charts for your answers into the document.
- Type your responses to the other questions.
- All of your charts, graphs, and responses to questions should be submitted in a single document.
MA 2025 Module 5 Statistics and Technology Assignment
1. The finishing times for a marathon requiring a qualifying time follow a normal distribution. A random sample of finishing times is given in the table below. Use the data below to calculate the 90% confidence interval for the population mean finishing time. Note the finishing times are given in minutes.
|
302 |
|
270 |
|
314 |
|
286 |
|
319 |
|
246 |
|
296 |
|
223 |
|
325 |
|
207 |
Find
a. The sample mean
b. The sample standard deviation
c. The sample size
d. The error bound of the mean
e. The 90% confidence interval for the population mean finishing time
2. A real estate company wants to estimate the mean selling price of a home in Chicago, Illinois. They randomly select the selling price of 50 homes sold in the previous month.
|
400000 |
590000 |
515000 |
300000 |
607000 |
|
720000 |
695000 |
700000 |
633000 |
314900 |
|
1190000 |
687500 |
440000 |
130000 |
390000 |
|
325000 |
1300000 |
320000 |
874999 |
442985 |
|
840000 |
747500 |
433000 |
530000 |
644000 |
|
325000 |
409000 |
645000 |
389999 |
810000 |
|
565000 |
355400 |
215000 |
1500000 |
925000 |
|
345000 |
799900 |
870000 |
677500 |
374000 |
|
615000 |
333000 |
420000 |
270500 |
606000 |
|
750000 |
495000 |
155000 |
285000 |
510000 |
a. Compute the following
b. Complete the chart below for each given confidence level. Round values to two decimal places.
|
Confidence Level |
Error Bound of the Mean |
Confidence Interval |
|
90% |
||
|
95% |
||
|
99% |
c. What happens to the error bound of the mean as the confidence level increases?
d. Use the list of home prices given to count how many of the data values lie within the 90% confidence interval. What percent is this? Is this percent close to 90%? Explain why this percent should or should not be close to 90%.
3. The following table shows the results of a survey in which 1105 adults from New York, 988 adults from Los Angeles, and 865 adults from Chicago were asked the question: “ Do you use public transportation at least once a week?”
|
Country |
Percentage That Responded “Yes” |
|
New York |
52% |
|
Los Angeles |
9% |
|
Chicago |
29% |
Construct and interpret a 98% confidence interval for
a. The population proportion of adults from New York who say they use public transportation at least once a week.
b. The population proportion of adults from Los Angeles who say they use public transportation at least once a week.
c. The population proportion of adults from Chicago who say they use public transportation at least once a week.