Posted: December 27th, 2014

Math Project "Sample Area" "Population

Math Project

“Sample
Area”    “Population
Standard
Deviation”    Confidence level %    “Level of Significance
α
”    “Hypothesis to test

“”The mean is actually”””
3        Rashed M+Ahmed Q+Abdulla M    Falaj Hazza    1.5476    90    0.1     less than the claimed value.

No    Name    “Bicarbonate,
18-23 mEqL”
1    Aaeda Abdulaziz E    16.190
2    Abdulla Ali Mohamed     19.150
3    Abdulla Juma Jaffar Hussain     27.540
4    Abdullah Khamis Mohamed     24.790
5    Abdulrasool Saleh    27.290
6    Abeer Rashed Saeed     18.390
7    Afra Belal Ismail     26.530
8    Ahlam Abdulla Mohamed    18.450
9    Ahmad Abdulla Ahmad     25.610
10    Ali Ahmed Sulaiman    25.170
11    Ali Mohamed Ali     18.530
12    Ali Mohammad Bin Tamim     23.550
13    Amal Hassan Abdulla     19.260
14    Amna Ali Saeed Mohammad     23.040
15    Asma Saleh Jaafar     23.970
16    Ayesha Abdulrazaq     22.790
17    Aysha Yousif Matar     27.020
18    Fatima Sulaiman Abdulla     16.270
19    Fatma Ahmad Ali Khalfan     23.950
20    Fatma Ahmad Ramadhan    28.000
21    Fatma Nasser Hussain     27.030
22    Fatma Salem Ahmad     24.880
23    Fuad Ahmed Mohaed     16.480
24    Hajar Humaid Salem     19.360
25    Hana Hussain Essa     24.530
26    Hanadi Mubarak     20.620
27    Hanifa Abdulfatah Hassan     21.410
28    Hassan Al Jaidi     27.110
29    Hend Abdulla Mohammad     21.280
30    Hessa Thani Mubarak     19.160
31    Iman Hussain Abdulla     18.620
32    Juma Sayed Abdulla     19.980
33    Laila Ahmad Mohamed     23.960
34    Latifa Abdulla Husain     27.960
35    Latifa Mubarak Bilal    24.230
36    Lubna Mohamed Sharif     18.640
37    Mahmood Ahmad Abdulrazzaq    28.060
38    Marwa Yousuf Mahmoud     19.610
39    Maryam Abdulhamid Moahmed     17.330
40    Maryam Hamad Obaid     19.870
41    Mira Ahmad Khalfan     19.730
42    Moammer Abdulla Saed Salem     18.480
43    Mohamed Ghanim    16.510
44    Mohammad Ali Jamil Al Balooshi     29.030
45    Mohammed Sulaiman Al Mehri     27.250
46    Mona Ahmed Mohamed Ali     26.850
47    Muna Ali Ahmad Mohammad     28.640
48    Nadia Abdulla Mohamed     26.520
49    Noora Ibrahim Mohaed Ahmad     25.540
50    Rashed Abdulla    30.000
51    Reem Omair Ali Omair     24.340
52    Saeed Mubarak Rashid     17.970
53    Saeed Salem Saeed     17.970
54    Sara Abdulla Ibrahim Mohamed     25.110
55    Sara Abdulla Mohamed Al Abdulla    16.510
56    Sarah Ali Abdulla Ahmad    16.180
57    Sulaiman Darwsh     24.480
58    Zainab Ali Ebrahim Ali     21.340
59    Rahman Ali    21.160
60    Muna Moammer    25.890

Zones    Falaj Hazza

A    2

B    0

C    1

D    1

E    4

F    4

G    2

H    2

I    3

J    2

K    1

L    1

M    0

N    1

O    4

P    0

Q    1

R    0

Sample Standard Deviation    1.3779

Higher Colleges of Technology
Al Ain Colleges

Names: ______________________________ ID#: __________________ Section: ____
Names: ______________________________ ID#: __________________ Section: ____
Names: ______________________________ ID#: __________________ Section: ____
Group #:   _____________________________

CIS 2003
Statistics and Probability
Case Study Analysis Project
Semester 1 2014-15

Weighting:                      15% of final semester grade
Due Date:                         4 pm, Sunday, 4th January, 2015
Instructions to students:     Read instructions on pages 2 & 3, for your hardcopy and softcopy Word file and Excel submission.
ACADEMIC HONESTY

Breaches of Academic Honesty will be treated with the utmost seriousness. You are reminded that the penalty for cheating or plagiarism is dismissal from HCT. It is

better to score zero than to be caught cheating.
Grade    % Range
A    90% – 100%
A-    85% – 89%
B+    80% – 84%
B    75% – 79%
C+    70% – 74%
C    65% – 69%
D    60% – 64%
F    59% and below

Total marks    50
Marks achieved        %

You will work with your group on this case analysis project. You are required to produce and submit an analysis to earn marks.  Marks earned are based on the attached

Student/Group Problem Answer Sheets for Parts 1 and 2.

You will be emailed assigned data sets, which will also be available on Blackboard Learn. The data was collected by healthcare professionals. This data is significant

to businesses because the health and welfare of all their employees and customers have a large impact on the productivity and profit margins of most companies.

Business managers are interested in factors which might be contributing to poor productivity.

Deadline
The case analysis is due 4pm,  Sunday, 4th January, 2015
Instructions for Students

Case Analysis Part 1 Objectives
•    CLO 1. Analyze the probability of given business outcomes using fundamental probability concepts for discrete and continuous probability distributions.
•    CLO 2. Apply concepts of sampling and the Central Limit Theorem in obtaining information that will facilitate the analysis of appropriate IT/business issues.

To complete the case analysis you will have to do the following:

1.    Use the data assigned in Dataset 1 to your group on the Student Problem Sheet by the instructor.

2.    Perform the following statistical tasks and enter all results onto the Student/Group Problem Answer Sheet.

3.    Submit the results.
The Student/Group Problem Answer Sheet should be filled out completely.

A hardcopy of the Student Problem Answer Sheet should be given to the instructor by the deadline. Please attach the coversheet of this document to your hardcopy, with

your group’s details completed.

A softcopy of the Student Problem Answer Sheet and Excel workbook should be emailed to the instructor by the deadline. Name your file as follows:  group name_class
Case Analysis Part 2 Objectives
•    CLO 3. Compute the probability of given IT/business outcomes by building one and two tailed confidence intervals for Z and t probability distributions.

•    CLO 4. Test different IT/business hypotheses by applying the concepts of confidence intervals, test statistics, p-value, type I and II errors, sample sizes,

and finite populations.

•    CLO 5. Draw statistical inferences from given IT/business information, based on one and two tailed hypothesis tests.

To complete the case analysis you will have to do the following:

1.    Use the data assigned in Dataset 2 to your group on the Problem Sheet by the instructor.

2.    Perform the assigned statistical tasks and enter all results onto the Answer Sheet.

3.    Submit the results.

The Answer Sheet should be filled out completely.

Give your instructor hard copies of the Rubric, the Problem Sheet and the Answer Sheet by the deadline and email soft copies of your Word and Excel workbook by the

deadline. Name your file: group name_class

Your group  will be emailed assigned data that is actual health data collected by health sciences professionals.  This data is significant to businesses because the

health and welfare of all employees have a large impact on the productivity and profit margins of most companies.  Business managers are interested in factors which

might be contributing to poor productivity.
Specifically, your data will be readings available from blood tests on 60 people. Data showing acceptable ranges for the readings are given on the first worksheet for

comparison purposes.

CIS 2003 – Statistics and Probability
Case Analysis Project Part 1
Student/Group Problem Answer Sheet
This form must be submitted with your Answer Sheet.

ACADEMIC HONESTY
Breaches of Academic Honesty will be treated with the utmost seriousness. You are reminded that the penalty for cheating or plagiarism is dismissal from HCT.  It is

better to score zero than to be caught cheating.

Name:  ______________________________  ID:  _______________________Sect:  ________

Name:  ______________________________  ID:  _______________________Sect:  ________

Name:  ______________________________  ID:  _______________________Sect:  ________

(1 mark)

Main cover page attached
(1 mark)

Assigned data:
Excel File – As emailed to students

Variable:  ___________________________                          (1 mark)

Part 1 – LOs 1 & 2

Part A
Descriptive Statistics- Population Parameters
Use the Data Set 1 provided to you by your Instructor (No Two Groups will use the Same Dataset)
a)    Use Megastat to summarize and present the Population using Descriptive Statistics (Mean, Median, Mode, Variance and Standard Deviation).

Insert a screen shot of the Megastat output which show the solutions.
(2 Marks)

b)    Use Megastat to present Population data graphically using a histogram.
Insert a screen shot of the Megastat output which shows the solution.
(2 Marks)
c)    Comment on the shape of the distribution. (Note: You may refer online to find out and compare the various shapes of a histogram.)
(2 Marks)

Part B

Normal Duistribution

a)    Assume your 60 readings to be a normally distributed population.  Use Excel to compute the population mean and the standard deviation and list them here:

µ = __________                                          σ = ___________
(2 marks)

Insert a screen shot of the Excel cells which show the functions and input values used for the computations of µ and σ.

(1 mark)

b)    The acceptable range for your data is given on the first worksheet of the Excel file.

Acceptable Range: ____________________________
(1 mark)

Estimate the number of readings (using Megastat) greater than the highest reading of your acceptable range.  Show your work for calculating the estimate. Provide the

actual number you count from your original data.
(2 marks)

Estimated: ________________________          Actual: ___________________________

Insert a screen shot of your Megastat results showing the input values used and your normal distribution curve with the percentage used in the estimation shaded.
(1 mark)

c)    According to the Empirical Rule, 68% of your data should be within one standard deviation of your population mean.

Based on the rule, find:

µ – ơ  ___________________
(1 mark)

µ + ơ  ____________________
(1 mark)

How many and what percentage of your readings are actually between those two readings?

Number: _________________________   Percentage:  _________________________

(2 marks)

d)    For a medical study, a researcher wishes to select people in the middle 40% of the population based on your readings.  Using your population mean and standard

deviation, find your upper and lower readings that would qualify people to participate in the study.

The lower reading to qualify is ___________________.
(1 mark)

The upper reading to qualify is ____________________.
(1 mark)

Insert a screen shot of your Megastat results showing the input values used and your normal distribution curve with the areas defined by the upper and lower readings

shaded.
(1 mark)

Part C

Sample Statistics

a)    Using your data in the order as originally given to you, select every 3rd reading from your data to create a sample of 20 readings.

Insert a screen shot from Excel of the sample you created.
(2 marks)

b)    Using the sample of 20 readings, determine the sample mean. The sample mean   = ________.
(1 mark)
Insert a screen shot of the Excel cells which show the functions and input values used for the computation of  .
(1 mark)

c)    Calculate the standard error of the mean.
(1 mark)

d)    Use the population mean and the standard deviation from Part A.   Determine the likelihood of a sample mean from your population of readings being less than  .
(1 mark)

Insert a screen shot of your Megastat results showing the input values used and your normal distribution curve with the probability shaded.
(1 mark)

e)    What method of sampling was used to get your 20 readings in (a)?
(1 mark)

f)    Calculate the sampling error of the mean.
(1 mark)

CIS 2003 – Statistics and Probability
Case Analysis Project Part 2
Student/Group Problem Sheet

This form must be submitted with your Answer Sheet.

ACADEMIC HONESTY
Breaches of Academic Honesty will be treated with the utmost seriousness. You are reminded that the penalty for cheating or plagiarism is dismissal from HCT. It is

better to score zero than to be caught cheating.

Name: ________________________________ ID:_________________ Sect: ___

Assigned data:
Excel File – As emailed to students.
Region – ______________
Part 2 – LOs 3, 4 & 5 – Confidence Intervals and Hypothesis Testing

Based on data collected over a particular four week period in several zones in regions of Abu Dhabi, the Abu Dhabi Food Control and Inspection Department claims the

number of food-borne illnesses having minor or severe outcomes per 100 people averages to 2.5042.   The population is normally distributed.
The population standard deviation is ______________.  The sample standard deviation is not to be used when the population standard deviation is known.

1)    Based on your sample, determine the best point estimate of your population mean.

2)    At the _________% level of confidence, develop a confidence interval for the population mean.

3)    At the α = ________ level of significance, can you conclude that:

______ the mean for your region is actually different from the claimed value?

______ the mean for your region is actually less than the claimed value?

______ the mean for your region is actually greater than the claimed value?

Fill in the Answer Sheet based on your work on #1, 2 and 3 above.

CIS 2003 – Statistics and Probability
Case Analysis Part 2 – Rubric

Fill in your name and submit this form with your Answer Sheet.

Name:___________________________________  ID: -_______________  Section:  ______

Name:___________________________________  ID: -_______________  Section:  ______

Name:___________________________________  ID: -_______________  Section:  ______

Item    Marks Allowed    Marks
Earned
Data presentation –
1.    Included Problem Sheet.
2.    Included Answer Sheet.
3.    Included screen shot of Megastat output.
4.    Soft copy file correctly named.
5.    Name on rubric filled out and rubric submitted to instructor.
1
1
1
1

1
Data Analysis –
1.    Gave correct point estimate.

2.    Correctly developed the appropriate confidence interval for the population mean.

3.    Stated the correct hypotheses.
4.    Used the correct critical value(s).
5.    Used the correct test statistic.
6.    Correctly interpreted the hypothesis test results.
7.    Answered question at bottom of Answer Sheet
1

2

3
2
3
1
1
Total    18

CIS 2003 –Statistics and Probability
Case Analysis Project Part 2 – Student/Group Answer Sheet

This form must be completed and submitted to earn marks.

Name:___________________________________ID:_______________Section: ___

= _____________   ơ = _____________    s = ______________   α = ___________

Point Estimate
ESTIMATED μ =

_____%
Confidence Interval
______________________ < μ < ¬¬¬¬¬¬¬¬¬¬¬¬¬¬_________________________

Hypotheses to Test
H0:

H1:

Critical Value(s)
z =_______________                     t = ______________
(Submit Megastat screen shot to show the critical value(s) output.)
Test Statistic
z =_______________                     t = ______________

Hypothesis Test Interpretation

________Reject H0                    ________Do not reject H0

Does your confidence interval contain your hypothesized mean? ____yes  ____no

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