## Statistics for Decision Making

MATH 399N Statistics for Decision Making

Week 6 iLab

Name:_______________________

Statistical Concepts:

• Data Simulation

• Confidence Intervals

• Normal Probabilities

Short Answer Writing Assignment

All answers should be complete sentences.

We need to find the confidence interval for the SLEEP variable. To do this, we need to find the mean and then find the maximum error. Then we can use a calculator to find the interval, (x – E, x + E).

First, find the mean. Under that column, in cell E37, type =AVERAGE(E2:E36). Under that in cell E38, type =STDEV(E2:E36). Now we can find the maximum error of the confidence interval. To find the maximum error, we use the “confidence” formula. In cell E39, type =CONFIDENCE.NORM(0.05,E38,35). The 0.05 is based on the confidence level of 95%, the E38 is the standard deviation, and 35 is the number in our sample. You then need to calculate the confidence interval by using a calculator to subtract the maximum error from the mean (x-E) and add it to the mean (x+E).

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets. (5 points)

Then, you can go down to cell E40 and type =CONFIDENCE.NORM(0.01,E38,35) to find the maximum error for a 99% confidence interval. Again, you would need to use a calculator to subtract this and add this to the mean to find the actual confidence interval.

2. Give and interpret the 99% confidence interval for the hours of sleep a student gets. (5 points)

3. 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. (10 points)

4. Find the mean and standard deviation of the DRIVE variable by using =AVERAGE(A2:A36) and =STDEV(A2:A36). 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. Use the formula =NORM.DIST(40, mean, stdev,TRUE). 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? (15 points)

Mean ______________ Standard deviation ____________________

Predicted percentage ______________________________

Actual percentage _____________________________

Comparison ___________________________________________________

______________________________________________________________

5. 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? Subtract the probabilities found through =NORM.DIST(70, mean, stdev, TRUE) and =NORM.DIST(40, mean, stdev, TRUE) for the “between” probability. To get the probability of over 70, use the same =NORM.DIST(70, mean, stdev, TRUE) and then subtract the result from 1 to get “more than”. Now determine the percentage of data points in the dataset that fall within this 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? (15 points)

Predicted percentage between 40 and 70 ______________________________

Actual percentage _____________________________________________

Predicted percentage more than 70 miles ________________________________

Actual percentage ___________________________________________

Comparison ____________________________________________________

_______________________________________________________________

Why? __________________________________________________________

________________________________________________________________

1) Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not

2) Consider the formula used for any confidence interval and the elements included in that formula. What happens to the confidence interval if you

A)increase the confidence level,

b)increase the sample size, or

C)increase the margin of error? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula.

3) How is the rejection region defined, and how is that related to the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?