SDM Applied Project 1
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Western University *
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Course
3316
Subject
Mathematics
Date
Jan 9, 2024
Type
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15
Uploaded by ChiefPheasantMaster1068
Page: 1 MATH1029 STATISTICAL DECISION MAKING APPLIED PROJECT TERM 1 2022 STUDENT NAME STUDENT ID SIGNATURE Harry 20186441 HN Khushi 20178332
KL Danny 20594493 DN Zarif 20474586 ZK Jacob 204488143 JD UNIT NAME: Statistical Decision Making UNIT NUMBER: MATH1029 NUMBER OF QUESTIONS: 4
VALUE OF QUESTIONS: Applied project questions are worth 40 marks in total. ANSWERING QUESTIONS: This applied project is to be completed using RStudio. All answers are to be typed or written on the space provided in this project. LECTURER/UNIT COORDINATOR: Rubie Herrera Michael Casey DUE DATE: Week 11: Friday, 27 May 2022, 11:59pm TOTAL PAGES: 15
INSTRUCTIONS TO STUDENTS •
The file containing the data sets for the following questions can be downloaded from the e-
learning site vUWS.
•
You should use RStudio to carry out all calculations and statistical analysis which must be
shown in the file to be submitted on vUWS. You will be required to submit the R-Script used to
perform all the calculations for all the questions. This R-Script should run without errors.
•
All answers in this booklet must match your calculations done and submitted in the R-Script.
•
To complete this project, you must provide the RStudio outputs for each of the questions.
•
Group projects submitted after the due date will attract a late penalty in accordance with the
late penalty policy stated on the Western Sydney University –
The College Website.
I-
II-
III-
IV-
Total: 34/
40
8.5
10
7
8.5
Good job, Group 3
!
Page: 2 To upload your R-Script file follow these instructions: a. Login to “vUWS”.
b. Select the Statistical Decision Making folder. c. Under the Assessment tab (from the left-hand side of the screen), select “Assessment 4: Applied Project (10%) and MATH1029 APPLIED PROJECT
2022.1”
. d. Use “Attach
files”
to select the file to be submitted. e. Double-check to make sure you have the correct file. f. “
Submit
”
your file.
Page: 3 Description of the assignment and data The assignment centers around a study of the academic performance of nursing students at the college during the previous term. The data in this file were gathered from nursing students at the college. The data stored in the Microsoft Excel file named Project Data 2022.1.xlsx is to be used for this assignment. It can be downloaded from vUWS. You are to use the data set assigned to your group to answer all the questionsin this assignment. The data set comprises of the following variables: Gender Gender of the participants: 1=Female 2=Male High School High school graduated from: 1= Public 2= Private Science End of term exam marks (in %) received in Science for Health Professionals Math End of term exam marks (in %) received in Math for Health Professionals Time Amount of time (in minutes) taken by the students to submit their end of term exam NOTE: The data was randomly created for the sole purpose of this assignment.
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Page: 4 The data can be found in the worksheet named Data& (“&
is the data numberassigned to your group) in the data file ProjectData 2022.1.
Page: 5 Question 1 - Khushi (ABC) a)
i). Mean = 64.29 ii). Median = 65 iii). Range = 60 you should have imported the Excel file instead 2
Page: 6 iv). Standard Deviation = 16.25 b)
Histogram: 2
frequency
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Page: 7 c)
In the dataset, my histogram shows that the highest number of students have scored between 60-70% in their end of term exam marks in Science for Health Professionals. All the other values for ‘amount of students’ are above 5 and close to 15 and values further away are rarer. The distribution is roughly symmetric and the values fall between approximately 40 and 90. A difference in means and median shifts the distributions horizontally along the X-axis, as the mean of 60 almost overlaps the median of 65. While the range falls between 30-90, the standard deviation of 16.25 centres the histogram for the nonnormal data that are skewed. Thus, the dataset shows which values are more and less common along with their dispersion. 64
1
Page: 8 d) Using RStudio, construct a 90% confidence interval for the population mean end of term exam mark in science for health professional during the previous terms * include the interpretation Population mean is between 61.9 and 66.6 based on 80 samples. Median: Male genders lay on 65 whereas Female lays on 60. Minimum:
Male genders with the lowest minimum score at 30 whereas Female lays at 35. Maximum: Maximum score for both genders are 90. Q1:
Both genders for Q1 are 50. Q3: Male Q3 is higher with the score of 79 whereas female is at 75. 1
0.5
We can be 90% confident
....
2
Page: 9 Question 2 (10 marks) - Zarif From the given information: a) R code: math<c(90,40,85,65,30,50,40,65,72,40,45,54,87,60,56,68,80,90,78,76,65,70,45,48,50,54,55,60,5 4,75,50,60,62,45,84,87,59,60,35,48,70,92,74,45,62,54,70,87,88,78,90,95,92,75,80,84,86,50,63,6 4,50,45,35,71,45,60,54,25,30,45,40,62,45,80,45,60,74,60,56,72) length(math) mean(math) sd(math) t.test(math, alternative="greater", mu=60, conf.int=0.95) OUTPUT: b) Using the information in the output, conduct a hypothesis test at a 5% level of significance. i) State the null and alternative hypothesis. 𝐻
0: 𝜇
= 60 𝐻𝑎
: 𝜇
> 60 ii) State the test statistic including the degrees of freedom. ? =
x
̅ − μ
?/√𝑛
= 1.2264
level
2
1
1
1
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Page: 10 𝑑𝑓
= 𝑛
− 1 = 80 − 1 = 𝟕𝟗
iii) State the decision rule. Reject Ho, if P-value is less than 0.05. iv) P-value = 0.1119 v) Decision: Since the P-value is greater than 0.05, so we fail to reject the null hypothesis. The result is not statistically significant at the 5% significance level. vi) Conclusion: Therefore, there is not sufficient evidence to support the claim that the average end of term exam mark is above 60% 1
1
1
1
1
Page: 11 Question 3 (10 marks) - Harry There are educational research showing various academic and non-academic factors related to academic performance of nursing undergraduates. You are interested in determining whether the high school graduated from is one among these factors. In this question, you are to investigate if there is a significant difference in the end of term exam mark in Mathematics for Health Professionals between nursing students who graduated from public and private high schools. a) Using RStudio, obtain an output for a hypothesis test at 10% level of significance. Assume that the mean differences are normally distributed. * [3] Pub=c(48, 50, 65, 50, 35, 74, 40, 65, 50, 65, 40, 54, 60, 56, 72, 78, 60, 62, 40, 68, 65, 90, 70, 50, 82, 74, 70, 65, 70, 67, 60, 65, 80, 87, 80, 90, 78, 65, 45, 54, 55, 60) Priv=c(74, 65, 52, 64, 87, 38, 90, 85, 30, 40, 72, 45, 87, 68, 75, 50, 58, 48, 80, 70, 70, 45, 75, 62, 90, 62, 80, 54, 70, 43, 48, 50, 76, 70, 48, 50, 54, 75) b) Using the information in the output, conduct a hypothesis test at a 10 % level of significance. alpha
or conf.level= 0.90
2
Page: 12 i)
State the null and alternative hypothesis. [1] 𝐻
0
: 𝜇 = 0
𝐻
𝑎
: 𝜇 ≠ 0
ii)
State the test statistic including the degrees of freedom. [2] T=
(63.15789−63.19048)−0
√
(16.00933)
2
38
+
(13.8533)
2
42
= -0.0096864 df = 73.622 iii)
State the decision rule. [1] Reject 𝐻
0
if P-value is greater or less than 0.10 iv)
State the p-value. [1] P-value=0.9923 v)
State the decision by giving reasons. [1] Since p value > 0.10 , reject 𝐻
0
vi)
Write down the conclusion. [1] There is not enough evidence at 10% level of significance to infer that there is a difference in exam marks between public and private high school graduates u1-u2=0
u1-u2 not =0
2
1
do not reject 1
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Page: 13 Question 4 (10 marks) - Jacob A college professor formed the theory that students who handed in quiz and exams early outperformed students who handed in their papers later. To develop data to decide whether her theory is valid, she recorded the amount of time (in minutes) taken by students to submit their end of term exam in Science for Health Professionals (time limit 150 minutes) and the subsequent mark for a sample of 80 students. (a)
Using RStudio, obtain linear regression outputs. * [4] 2
Time
Science
2
Page: 14 (b)
Determine the linear regression equation that may be used to predict the final exam mark of a student who took 95 minutes before submitting the final exam paper. * [2] All students linear regression equation y = 149.5929 –
0.8987x students who took 95 minutes linear regression equation y = 117.38489 - 0.54801 c)
Interpret the slope of the regression line. * [1] B1= -0.8987 For every minute a student takes to hand in the quiz their score will drop by 0.8987 marks d)
State and interpret the coefficient of determination. * [2] The coefficient of determination is 0.4925 49.54% of the variability of the time taken can be explained by the variability of the students’ marks.
1-
?
2
=1-0.4925=0.5075 coefficient of non-determination (e) State the correlation coefficient. * [1] r= √R² = -
√0.4925 = -0.7018 y=?
1
1
1
0.5
mark
time
1
Page: 15 Student declaration: We declare that all submitted answers are our own work, no part of this exam has been copied from anyone else and we have not shared our work with any other students. Name Student ID Signature Harry 20186441 HN Khushi 20178332 KL Danny 20594493 DN Zarif 20474586 ZK Jacob 204488143 JD
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