Download Math 224 – Elementary Statistics

STATISTICS – LAB #6
Statistical Concepts
 Data Simulation
 Discrete Probability Distribution
 Sampling Distribution
 Central Limit Theorem
Calculations for a set of observations
 Open the class survey results that were entered into the MINITAB worksheet.
 We want to calculate the mean for the 10 rolls of the die for each student in the class.
Label the next column in the Worksheet with the word mean. Pull up Calc > Row
Statistics and select the radio-button corresponding to Mean. For Input variables:
enter all 10 rows of the die data. Go to the Store result in: and select the mean
column. Click OK and the means for each observation will show up in the
Worksheet.
 We also want to calculate the median for the 10 rolls of the die. Label the next
column in the Worksheet with the word median. Repeat the above steps but select
the radio-button that corresponds to Median and in the Store results in: text area,
place the median column.
Calculating Descriptive Statistics
 Calculate descriptive statistics for the mean and median columns that where created
above. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set
Variables: to mean and median. The output will show up in your Session Window.
Print this information.
Simulating Data
 Open a new MINITAB worksheet.
 We are going to use a continuous distribution called the exponential with a mean and
standard deviation of one to illustrate the affect of sample size on a sampling
distribution. Pull up Calc > Random Data > Exponential and enter 100 for the
Number of rows of data to generate:. For Store in column(s): enter C1 and click
OK. Note: This data represents the exponential along with the sampling distribution
with a sample size of one. Create a histogram for this column and print out a copy.
Title the graph (with your name and n = 1).
 Open a new MINITAB worksheet.
 Pull up Calc > Random Data > Exponential and enter 100 for the Number of rows
of data to generate:. For Store in column(s): enter C1-C5 and click OK. Label
column C6 with the word mean and do row statistics (same as before) to calculate
the mean for each row. Create a histogram for this column and print out a copy.
Title the graph (with your name and n = 5).
 Open a new MINITAB worksheet.
 Pull up Calc > Random Data > Exponential and enter 100 for the Number of rows
of data to generate:. For Store in column(s): enter C1 - C30 and click OK. Label
column C31 with the word mean and do row statistics (same as before) to calculate
the mean for each row. Create a histogram for this column and print out a copy.
Title the graph (with your name and n = 30).
Short Answer Writing Assignment
If applicable, answers should be complete sentences. Include copies of all print outs
with this assignment.
1. When rolling a die, is this an example of a discrete or continuous random variable? Explain your
reasoning via the properties of this type of variable.
2. Calculate the mean and standard deviation of the probability distribution created by rolling a die.
3. Give the mean for the mean column of the Worksheet. Is this estimate centered about the
parameter of interest (answer in question 2)?
4. Give the mean for the median column of the Worksheet. Is this estimate centered about the
parameter of interest (answer in question 2)?
5. Does the mean or median column have a lower standard deviation?
6. Is the mean or median a better estimate for the center of this distribution? Explain your reasoning.
7. Explain the shape of the following histograms with the exponential as the underlying distribution:
a. Sample size = 1
b. Sample size = 5
c. Sample size = 30
8. What does the shape of these histograms tell us about sample size for a sampling distribution (think
about the Central Limit Theorem)?