Statistical Concepts:

Data Simulation

Confidence Intervals

Normal Probabilities

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. First, find the standard deviation by Stat > Basic Statistics > Display Descriptive Statistics and set the variable to Sleep, and in “statistics” be sure standard deviation is selected. Click OK and OK and write down the standard deviation. Pull up Stat > Basic Statistics > 1-Sample z and set Samples in columns: to Sleep. Type in the standard deviation. Click the OK button and the results will appear in your Session Window.

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.

Give and interpret the 95% confidence interval for the hours of sleep a student gets. 

Give and interpret the 99% confidence interval for the hours of sleep a student gets.

Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs.)

In the week 2 lab, you found the mean and the standard deviation for the HEIGHT variable for both males and females. Use those values or follow these directions to calculate the numbers again.

First, find the number, mean, and standard deviation by Stat > Basic Statistics > Display Descriptive Statistics and set the variable to Height and in “by group” select “Gender”. In “statistics” be sure mean and standard deviation are selected. Click OK and OK.

Find the 95% confidence interval for the height of females by clicking on Stat > Basic Statistics > 1-Sample t. Use the “Summarized data” section and type in the values found in the step above. Click on “options” and put in 95 for the level of confidence. Click the OK and OK and the results will appear in your Session Window. To find the 99% confidence interval, do the same steps, but type in 99 for the level of confidence in the options window. The same steps can be followed for the male data.

Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable. Which is wider and why? (7 points)

Give and interpret the 99% confidence intervals for males and females on the HEIGHT variable. Which is wider and why? (7 points)

Find the mean and standard deviation of the DRIVE variable by using Stat > Basic statistics > Display descriptive statistics and set the variable to DRIVE (without any group variable). Under “statistics” be sure mean and standard deviation are checked. Then click OK and OK. Assuming that this variable is normally distributed, what percentage of data would you predict would be less than 40 miles? This would be based on the calculated probability. In Minitab, go to Calc > Probability distributions > Normal and click “cumulative probability” and in “variables” put DRIVE. In the input constant, type 40 and the probability of less than 40 will show in the session window. Now determine the percentage of data points in the dataset that fall within this range. To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points. That is the actual percentage. How does this compare with your prediction? (10 points)

Mean ______________ Standard deviation ____________________

Predicted percentage ______________________________

Actual percentage _____________________________

Comparison ___________________________________________________

______________________________________________________________

What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? First, the probability for less than 70 by using the same steps as above, but using 70 as the input constant. To find “between 40 and 70”, use a calculator to take the probability of “less than 70” and subtract the probability of “less than 40” from above. To find “more than 70”, use a calculator to subtract the probability of less than 70 from 1 to get “more than”. Now determine the percentage of data points in the dataset that fall within each range, using same strategy as above for counting data points in the data set. How do each of these compare with your prediction and why is there a difference? (11 points)

Predicted percentage between 40 and 70 ______________________________

Actual percentage _____________________________________________

Predicted percentage more than 70 miles ________________________________

Actual percentage ___________________________________________

Comparison ____________________________________________________

_______________________________________________________________

Why? __________________________________________________________

________________________________________________________________

Answer rating: 100% (QA)

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