Question

In this project you will: hand in a formal memo with worksheet attached (showing your work, calculations by-hand) 1. 2. Calculate relevant descriptive statistics Create a formal memorandum describing results - should be formatted properly and include a bar graph representing the means of the two groups (that includes your name) - should include a table of relevant descriptive statistics: Mean, median and modes for number of errors for each group Standard deviation and range as well as minimum and maximum number of errors for each group - should include a call to action, or recommendation on whatthe administrator should do about the shift times - should include a statement about the highest and lowest perform ing nurses (who made most and fewest number of errors) Imagine an administrator in a large hospital has hired you as a consultant. Some of the nursing staff work 12-hour shifts, while other nurses work 8-hour shifts. Generally, research suggests there are pros and cons for each of these shift durations. The advantages to the longer 12 hour shifts include better family relations, better physical and psychological feelings of welbeing, and better off-duty sleep. The disadvantages include fatigue, increased errors in patient care, and increased likelihood oftraffic accidents following the longer shifts. You are especially concerned about the impairment in patient care, so you ran a small study. You randomly assigned nurses to two different shift durations (8-hour versus 12-hour shifts) and you measured the numbers of errors made for one month. The results you found are presented below. Please calculate the requested descriptive statistics. These will be used to help you write a memo hospital administrator 8-hour shift Stan made 3 Kyle made 6 Eric made 8 Sheila made 4 rdi res r findin ardedW Sharon made Liane made 8 lke made 2 Peter made 4 Henrietta made Laura made 4 Sum- E(x- Standard Deviation Mean- Min Score- Median- Max Score- Mode- Range 12-hour s hift Heidi made Amber made 8 Kenny made 5 Hollis made 5 lora made Anne made 6 Conner made 5 Filmore made 9 Donald made 7 Ellen made 1 Sum Standard Deviation Mean = Min Score- Median Max Score- Mode- Range

Answer 1

	8 Hour shift	$(X - \bar{X})$	$(X - \bar{X})^{2}$
	3	-2	4
	6	1	1
	8	3	9
	4	-1	1
	5	0	0
	8	3	9
	2	-3	9
	4	-1	1
	6	1	1
	4	-1	1
Total	50	0	36

Sum = Sum of error = 50

$\Sigma (X - \bar{X})$ = 0

$\Sigma (X - \bar{X})^{2}$ = 36

Standard Deviation = $\sqrt{\Sigma (X - \bar{X})^{2} / n }$ = $\sqrt{36 / 10}$ = 1.8974

S = $\sqrt{\Sigma (X - \bar{X})^{2} / n-1 }$ = $\sqrt{36 / 9}$ = 2.0000

Mean $\bar{X}$ = $\Sigma X_{i}/n = 50 / 10 = 5$

Median = Middle most value that are arrange in ascending order = 5^th & 6^th value

taking the average of it = ( 4 + 5 ) / 2 = 4.5

Median = 4.5

Mode = is the value occure most frequently = 4 ( 4 occurs 3 times in the data)

Minimum score = 2

Maximum score = 8

Range = Maximum - Minimum = 8 - 2 = 6

For 12 Hour Shift

	12 hour shift	$(X - \bar{X})$	$(X - \bar{X})^{2}$
	5	-1	1
	8	2	4
	5	-1	1
	5	-1	1
	9	3	9
	6	0	0
	5	-1	1
	9	3	9
	7	1	1
	1	-5	25
Total	60	0	52

Sum = Sum of error = 60

$\Sigma (X - \bar{X})$ = 0

$\Sigma (X - \bar{X})^{2}$ = 52

Standard Deviation = $\sqrt{\Sigma (X - \bar{X})^{2} / n }$ = $\sqrt{52 / 10}$ = 2.2804

S = $\sqrt{\Sigma (X - \bar{X})^{2} / n-1 }$ = $\sqrt{52 / 9}$ = 2.4037

Mean $\bar{X}$ = $\Sigma X_{i}/n = 60 / 10 = 6$

Median = Middle most value that are arrange in ascending order = 5^th & 6^th value

taking the average of it = ( 5 + 6 ) / 2 = 5.5

Median = 5.5

Mode = Is the value occure most frequently = 5 ( 5 occurs 4 times in the data)

Minimum score = 1

Maximum score = 9

Range = Maximum - Minimum = 9 - 1 = 8

Comparison Table	8 - hour	12 - hour
Mean error	5	6
Median error	4.5	5.5
Mode error	4	5
SD of error	1.8974	2.2804
Minimum error	2	1
Maximum error	8	9
Range of error	6	8

• In 8 - hour shift, mean error is less than 12 - hour shift
• standard deviation of error in 8 - hour shift is less than 12 - hour shift, so 8-hour shift is recommended
• Maximin error in 8 - hour shift is less than 12 - hour shift
• Range of error in - horu shfit is less than 12 - hour shift

Overall 8 - hour shift is better than 12 - hour shift, in term of performance.