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.

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets. Change the confidence level to 99% to find the 99% confidence interval for the SLEEP variable.

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.

(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.

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

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

6. 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 ___________________________________________________ ______________________________________________________________

7. 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? __________________________________________________________ ________________________________________________________________

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

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

Answer 1

Excel output:

Sleep (hours)		Column1			Column1
7
7		Mean	7.2		Mean	7.2
5		Standard Error	0.238341609		Standard Error	0.238342
7		Median	7		Median	7
6		Mode	8		Mode	8
8		Standard Deviation	1.410047976		Standard Deviation	1.410048
7		Sample Variance	1.988235294		Sample Variance	1.988235
8		Kurtosis	0.492339363		Kurtosis	0.492339
5		Skewness	-0.510056314		Skewness	-0.51006
8		Range	6		Range	6
8		Minimum	4		Minimum	4
4		Maximum	10		Maximum	10
8		Sum	252		Sum	252
8		Count	35		Count	35
6		Confidence Level(95.0%)	0.484368424		Confidence Level(99.0%)	0.65029
8
8		95% confidence interval			99% confidence interval
8		Lower limit = mean - confidence level	6.715631576		Lower limit = mean - confidence level	6.54971
7		Upper limit = mean + confidence level	7.684368424		Upper limit = mean + confidence level	7.85029
10
6
7
8
5
8
7
7
4
9
8
7
7
8
8
10

1. Enter data in excel.

2. Go to data menu --> select 'Data Analysis' option in the upper right corner

3. select descriptive statistic option. By default confidence level is 95%. To get 99% confidence interval enter confidence level 99.

Que.1 95% confidence interval is (6.7156, 7.6844)

Interpretation:

If we compute 100 such intervals then at least 95 confidence intervals will contain the true value of average sleep hours.

Que.2  

99% confidence interval is (6.5497, 7.8502)

Interpretation:

If we compute 100 such intervals then at least 99 confidence intervals will contain the true value of average sleep hours.

Que.3

We see that 99% confidence interval is more wider than 95% confidence interval.

This is because as we increase confidence level then margin of error () also increases and ultimately length of confidence interval increases.

Please provide information of gender and drive variable to answer remaining question