Question

We need to find the confidence interval for the SLEEP 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.

First, find the mean and standard deviation by copying the SLEEP 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. The confidence interval is shown in the yellow cells as the lower limit and the upper limit.

Sleep (hours)
7
7
5
7
6
8
7
8
5
8
8
4
8
8
6
8
8
8
7
10
6
7
8
5
8
7
7
4
9
8
7
7
8
8
10

  

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets.
2. Give and interpret the 99% confidence interval for the hours of sleep a student gets
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.

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 for follow these directions to calculate the numbers again.

Height (inches)
61
62
63
63
64
65
65
66
66
67
67
67
67
68
68
69
69
69
69
69
69
69
70
70
70
70
70
71
71
71
73
73
74
74
75

(From Week 2 Lab: Calculate descriptive statistics for the variable Height by Gender. Click on Insert and then Pivot Table. Click in the top box and select all the data (including labels) from Height through Gender. Also click on “new worksheet” and then OK. On the right of the new sheet, click on Height and Gender, making sure that Gender is in the Rows box and Height is in the Values box.   Click on the down arrow next to Height in the Values box and select Value Field Settings. In the pop up box, click Average then OK. Write these down. Then click on the down arrow next to Height in the Values box again and select Value Field Settings. In the pop up box, click on StdDev then OK. Write these values down.)

You will also need the number of males and the number of females in the dataset. You can either use the same pivot table created above by selecting Count in the Value Field Settings, or you can actually count 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 females on the HEIGHT variable. Which is wider and why?

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

3. 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 percentage of data points from that data set that we would expect to be less than 40. 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?

Mean ______________             Standard deviation ____________________ Predicted percentage ______________________________ Actual percentage _____________________________ Comparison ___________________________________________________ ______________________________________________________________

4. 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? Use the Week 4 spreadsheet again to find the percentage of the data set we expect to have values between 40 and 70 as well as for more than 70. 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?

Predicted percentage between 40 and 70 ______________________________ Actual percentage _____________________________________________ Predicted percentage more than 70 miles ________________________________ Actual percentage ___________________________________________ Comparison ____________________________________________________ _______________________________________________________________ Why? __________________________________________________________ ________________________________________________________________

Answer 1

Week 1 spreadsheet.

	Sleep ( X )
	7	0.04
	7	0.04
	5	4.84
	7	0.04
	6	1.44
	8	0.64
	7	0.04
	8	0.64
	5	4.84
	8	0.64
	8	0.64
	4	10.24
	8	0.64
	8	0.64
	6	1.44
	8	0.64
	8	0.64
	8	0.64
	7	0.04
	10	7.84
	6	1.44
	7	0.04
	8	0.64
	5	4.84
	8	0.64
	7	0.04
	7	0.04
	4	10.24
	9	3.24
	8	0.64
	7	0.04
	7	0.04
	8	0.64
	8	0.64
	10	7.84
Total	252	67.6

Mean

Standard deviation

Confidence Interval



Lower Limit =
Lower Limit = 6.7156
Upper Limit =
Upper Limit = 7.6844
95% Confidence interval is ( 6.7156 , 7.6844 )

Margin of error =  

Confidence Interval



Lower Limit =
Lower Limit = 6.5497
Upper Limit =
Upper Limit = 7.8503
99% Confidence interval is ( 6.5497 , 7.8503 )

Margin of error =

Part c)

Margin of error for 99% confidence interval is greater than 95%.

Hence 99% confidence interval is wider than 95% confidence interval.