Statistical Concepts:

Data Simulation

Discrete Probability Distribution

Confidence Intervals

Calculations for a set of variables

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 column next to die10 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 mean 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.

Mean Median

3.2 3.5

4.5 5.0

3.7 4.0

3.7 3.0

3.1 3.5

3.6 3.5

3.1 3.0

3.6 3.0

3.8 4.0

2.6 2.0

4.3 4.0

3.5 3.5

3.3 3.5

4.1 4.5

4.2 5.0

2.9 2.5

3.5 4.0

3.7 3.5

3.5 3.0

3.3 4.0

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.

Descriptive Statistics: Mean, Median

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum

Mean 20 0 3.560 0.106 0.476 2.600 3.225 3.550 3.775 4.500

Median 20 0 3.600 0.169 0.754 2.000 3.000 3.500 4.000 5.000

Calculating Confidence Intervals for one Variable

Open the class survey results that were entered into the MINITAB worksheet.

We are interested in calculating a 95% confidence interval for the hours of sleep a student gets. Pull up Stat > Basic Statistics > 1-Sample t and set Samples in columns: to Sleep. Click the OK button and the results will appear in your Session Window.

One-Sample T: Sleep

Variable N Mean StDev SE Mean 95% CI

Sleep 20 6.950 1.572 0.352 (6.214, 7.686)

We are also interested in the same analysis with a 99% confidence interval. Use the same steps except select the Options button and change the Confidence level: to 99.

One-Sample T: Sleep

Variable N Mean StDev SE Mean 99% CI

Sleep 20 6.950 1.572 0.352 (5.944, 7.956)

Short Answer Writing Assignment

All answers should be complete sentences.

When rolling a die, is this an example of a discrete or continuous random variable? Explain your reasoning.

When rolling a die is an example of a discrete random variable since rolling a die, we only have a 1/6 chances when rolling a number. Besides is always a concrete number it is never a 1.0001 chances.

Calculate the mean and standard deviation of the probability distribution created by rolling a die. Either show work or explain how your answer was calculated.

Mean: 3.450 Standard deviation: 1.317

Give the mean for the mean column of the Worksheet. Is this estimate centered about the parameter of interest (the parameter of interest is the answer for the mean in question 2)?

Mean : 3.560

Give the mean for the median column of the Worksheet. Is this estimate centered about the parameter of interest (the parameter of interest is the answer for the mean in question 2)?

Men is 3.600

Give the standard deviation for the mean and median column. Compare these and be sure to identify which has the least variability?

Standard deviation for the mean is 0.476 and for the median is...