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## Standard Scores Questions

1. Use both the Student ID and Distance to Work variables.
2. List the Student ID at TESU in ascending order of Distance to Work.
3. Calculate the z-scores associated with each student (use the sample standard deviation for this calculation).
4. Identify potential outliers and explain your reasoning.
 ID Distance to Work (whole miles) Z-Score 18 0 (1.07) 9 0 (1.07) 2 0 (1.07) 12 0 (1.07) 1 0 (1.07) 21 2 (0.92) 3 5 (0.69) 20 6 (0.62) 11 7 (0.54) 17 8 (0.47) 15 10 (0.31) 4 10 (0.31) 23 12 (0.16) 22 15 0.06 19 15 0.06 5 15 0.06 10 20 0.44 14 25 0.82 6 30 1.19 7 32 1.34 8 36 1.65 16 38 1.80 13 40 1.95

There are no potential outliers as all the z-values consists of -2 and 2.

## Confidence Intervals

1. Take a sample of the first four data points for the variable Distance to Work (unsorted - use the original order in the dataset).
2. Determine the 95% and 99% confidence intervals using the same size of 4.
3. Describe and compare the two intervals.

#### Solution

The confidence interval for 4-points is[x ̅-t_(1-α/2,3)×s/√4,x ̅+t_(1-α/2,3)×s/√4]
Mean = 3.75
Std Dev = 4.787
t-value for 95% CI = 3.182
t-value for 99% CI = 5.841
 95% Confidence Interval Lower (3.87) Upper 11.37 99% Confidence Interval Lower (10.23) Upper 17.73
The 99% Confidence interval is wider than 95% Confidence interval which is expected. The CI also contains negative value,which is absurd, but this has been estimated assuming normal distribution as underlying distribution and hence, contains negative values.

Take a sample of the first seven data points for the variable Distance to Work (unsorted - use the original order in the dataset).
Determine the 95% confidence interval. Use the same mean and SD, but change the sample size to 20 and determine the 95% confidence interval.
Describe and compare the two intervals.
The confidence interval for 20-points is [x ̅-t_(1-α/2,19)×s/√20,x ̅+t_(1-α/2,19)×s/√20]
 Mean 16.00 Std Dev 14.75 N 20.00 t-value 2.09 95% CI Lower 9.10 Upper 22.90

This interval is a lot narrower than the last ones. This is because the sample size is large which reduces the standard error of the mean and the t-value for large degrees of freedom is close to normal and smaller than the t-value of smaller degrees of freedom.

## Student Database

 ID School Enrolled Months Enrolled Birthday Month Distance to Work (whole miles) Height (whole inches) Foot Size (whole inches) Hand Size (whole inches) Sleep (minutes) Homework (minutes) 1 Arts and Sciences 12 January 0 60 8 5 360 30 2 Applied Science and Technology 6 February 0 62 7 6 400 45 3 Business and Management 8 April 5 66 10 7 420 60 4 Nursing 10 June 10 68 12 8 440 15 5 Public Service 48 July 15 68 14 8 540 75 6 Arts and Sciences 48 June 30 70 12 9 480 120 7 Applied Science and Technology 36 October 32 72 11 8 320 80 8 Applied Science and Technology 32 November 36 75 14 7 440 60 9 Business and Management 3 May 0 67 10 7 360 180 10 Business and Management 3 January 20 62 7 6 360 180 11 Applied Science and Technology 32 January 7 69 10 7 420 180 12 Applied Science and Technology 11 April 0 67 11 8 390 210 13 Applied Science and Technology 3 March 40 68 9 6 480 120 14 Applied Science and Technology 6 December 25 69 11 7 390 150 15 Applied Science and Technology 7 December 10 74 11 8 450 120 16 Applied Science and Technology 1 January 38 67 10 7 360 150 17 Business and Management 36 December 8 65 10 7 360 210 18 Business and Management 1 June 0 66 7 7 360 120 19 Applied Science and Technology 14 July 15 70 10 8 420 120 20 Applied Science and Technology 12 January 6 73 11 8 480 120 21 Applied Science and Technology 12 December 2 69 11 8 390 120 22 Applied Science and Technology 12 April 15 73 11 8 420 180 23 Applied Science and Technology 1 August 12 70 11 7 300 240
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