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MATH 221 Confidence Intervals & Probabilities Exercises

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MATH221 Statistics for Decision Making
Week 6 Lab
Name:_______________________
Statistical Concepts:
Confidence Intervals
Data Simulation
Normal Probabilities
Short Answer Writing Assignment
All answers should be complete sentences.
In the Week 2 Lab, you found the mean and the standard deviation for the SLEEP
variable for both males and females. Use those values for follow these directions to
calculate the numbers again.
(From Week 2 Lab: Calculate descriptive statistics for the variable Sleep by Gender.
Sort the data by gender by clicking on Data and then Sort. Copy the Sleep of the
males from the data file into the Descriptive Statistics worksheet of the Week 1 Excel
file. [Write down the mean and standard deviation.] These are sample data. Then,
copy and paste the female data into the Descriptive Statistics workbook and do the
same. Keep three decimal places.)
You will also need the number of males and the number of females in the dataset. You
can actually count these in the dataset.
Then use the Week 5 spreadsheet to calculate the following confidence intervals. The
male confidence interval would be one calculation in the spreadsheet and the females
would be a second calculation.
1. Give and interpret the 95% confidence intervals for males and a second 95% confidence
interval for females on the SLEEP variable. Which is wider and why?
95% confidence interval for males- (6.811,8.719)
Width of the confidence interval = 1.908
95% confidence interval for females- (6.733,8.601)
Width of the confidence interval = 1.869
The confidence interval for males is wider as the group has a lower number of
observations (n=17) compared to females (n=18) and hence have a higher margin of
error despite having slightly lower standard deviation compared to the females group.
2. Give and interpret the 99% confidence intervals for males and a second 99% confidence
interval for females on the SLEEP variable. Which is wider and why?

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99% confidence interval for males- (6.451,9.079)
Width of the confidence interval = 2.628
99% confidence interval for females- (6.383,8.951)
Width of the confidence interval = 2.567
The confidence interval for males is wider as the group has a lower number of
observations (n=17) compared to females (n=18) and hence have a higher margin of
error despite having slightly lower standard deviation compared to the females group.
We need to find the confidence interval for the SHOE SIZE variable. To do this, we
need to find the mean and standard deviation with the Week 1 spreadsheet. Then we can
the Week 5 spreadsheet to find the confidence interval. This does not need to be
separated by males and females, rather one interval for the entire data set.
First, find the mean and standard deviation by copying the SHOE SIZE variable and
pasting it into the Week 1 spreadsheet. Write down the mean and the sample standard
deviation as well as the count. Open the Week 5 spreadsheet and type in the values
needed in the green cells at the top to find the confidence interval.
3. Give and interpret the 95% confidence interval for the size of students’ shoes.
95% confidence interval for the size of the students’ shoes- (7.854,9.346)
We are 95% confident that the mean size of all student’s shoes lies between 7.854 and
9.346.
Change the confidence level to 99% to find the 99% confidence interval for the SHOE
SIZE variable.
4. Give and interpret the 99% confidence interval for the size of students’ shoes.
99% confidence interval for the size of the students’ shoes- (7.598,9.602)
We are 99% confident that the mean size of all student’s shoes lies between 7.598 and
9.602.
5. Compare the 95% and 99% confidence intervals for the size of students’ shoes. Explain
the difference between these intervals and why this difference occurs.
The 99% confidence interval is wider than the 95% confidence interval. Because we are
more confident that the mean size of all student’s shoes lies in the former interval, the
former is wider than the latter.
6. Find the mean and standard deviation of the DRIVE variable by copying that variable
into the Week 1 spreadsheet. Use the Week 4 spreadsheet to determine the

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1 MATH221 Statistics for Decision Making Week 6 Lab Name:_______________________ Statistical Concepts: • Confidence Intervals • Data Simulation • Normal Probabilities Short Answer Writing Assignment All answers should be complete sentences. In the Week 2 Lab, you found the mean and the standard deviation for the SLEEP variable for both males and females. Use those values for follow these directions to calculate the numbers again. (From Week 2 Lab: Calculate descriptive statistics for the variable Sleep by Gender. Sort the data by gender by clicking on Data and then Sort. Copy the Sleep of the males from the data file into the Descriptive Statistics worksheet of the Week 1 Excel file. [Write down the mean and standard deviation.] These are sample data. Then, copy and paste the female data into the Descriptive Statistics workbook and do the same. Keep three decimal places.) You will ...
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