Statistics

2. INTRODUCTION

2.1 Problem Definition

Stress has been a prominent factor in all of our lives due to the complications of living in a fast-paced society. Music therapy is increasingly gaining acceptance globally in schools as a legitimate modality for healing stress related problems. The purpose of this report is to elicit the reactions of the respondents towards having music therapy services at National University of Singapore (NUS).

2.2 Method of Investigation

Interviews and surveys are conducted by our group based on a stratified sample of 160 personnel(students & staffs) in total, from ten major faculties in NUS. These personnel were selected through the use of the non-probability sample of convenience sampling. All the raw data we gathered was analysed in order to obtain meaning to our findings.

We have also assessed the potential of using tools such as Bar Charts, Scatter Diagram Process Charts and Hypothesis Testing for our analysis. Research using textbooks and the Internet had also been done to gather more information on the uncertain topics. In addition, we consulted our tutor for advice and clarified any queries.

2.3 Description Of Data

In order to calculate the population proportion, p within our desired confidence interval of 95% and our acceptable sampling error, e of 0.08, we need to determine the sample size for p. Assumption: Ps = 0.50 (to be verified later using Hypothesis Testing),

For 95% confidence interval, Z0.025 = 1.96 and P is estimated by using Ps = 0.50

n = (Z0.025) 2 Ps (1-Ps) = (1.96) 2 0.50 (0.50)

e2 (0.08)2

N = 150.0625 = 151 (The general rule is to slightly oversatisfy the criteria by rounding the sample size up to the next whole integer.)

Therefore, a sample size of 151 would be necessary if we want to estimate the true proportion willing to go for music therapy in a large population within + 8 %, with 95% confidence.

Next, out of the sample size of 151, the number of teaching staff and undergraduate students needed are then obtained as below:

Designation NUS population Sample Size

Faculty teaching staff 2,158 151 (2158 / 25,252) =12.90 = 13

Undergraduate Students 23,094 (See Appendix A) 151 (23,094 / 25,252) =138.10=139

Total 25,252 152

Assumption: The teaching staff population also follows the distribution pattern in the pie chart. In other words, if 22% of the population of students is from FASS, 22% of the population of teaching staff will also be from FASS.

Finally, based on the pie chart (See Appendix A), the percentage of students from each faculty out of the NUS population is known and the number of teaching staff and undergraduate students needed from each faculty is then obtained as below:

All Faculties & Schools Teaching Staff Undergraduate Students

FASS 22% 0.22*12.90 = 2.839 = 3 0.22*138.10= 30.381 =31

Bizad 5% 0.05*12.90 = 0.645= 1 0.05*138.10= 6.905= 7

SOC 8% 1.032= 2 10.975 = 11

Dentistry 1% 0.129=1 1.381= 2

SDE 7% 0.903 = 1 9.667 = 10

Engineering 27% 3.484=4 37.286= 38

Law 4% 0.516 = 1 5.524 = 6

Science 20% 2.581 = 3 27.619 = 28

Medicine 5% 0.645= 1 6.905= 7

Music 1% 0.129=1 1.381= 2

Total 18 142

Note: The general rule is to slightly oversatisfy the criteria by rounding the numbers up to the next whole integer. Thus, n is no longer 151,n = 18+142 = 160 instead.

3. FINDINGS

3.1 Probability Comparison

One of the important information that we are concerned in this report is the chances of teaching staffs and students who are willing to go for music therapy service, and their willingness to pay. Below is our table of results, gathered from 142 students and 18 teaching staffs.

Table 1: Comparison between Teaching Staffs and Students of their Willingness to Go for Music Therapy Service.

Willing to Go Music Therapy (G) Designation Total

Teaching Staff (T) Students

(S)

Yes 11 81 92

No 7 61 68

18 142 160

To study the results of the percentage of those who are being surveyed on whether they are willing to for music therapy service, probability is the best method used to compare these event. First of all, we would like to find out the probability of students and teaching staff who are willing to go for music therapy service.

G: Willing to go for music therapy service S: Students

T: Teaching Staffs M: Willing to pay

P (G) = 92/160 or 0.575

P (G | T) = P (G and T) / P(T)

= 11/18 or 0.6111

P (G | S) = P (G and S) / P (S)

= 81/142 or 0.5704

With the calculations above, there is an approximately 57.5% chance that those respondents will go for music therapy service. Therefore, the recommendation to provide music therapy service in NUS is feasible. Out of those people who are being surveyed, it shows that 61.11% chance that teaching staff are willing to go for the service while 57.04% chance that students who are willing to go. Hence, it shows that teaching staff are more willing to go for music therapy service than students.

Table 2: Comparison between Teaching Staffs and Students of their Willingness to Pay

Willing to Pay

(M) Designation Total