Statistical research on gambling behaviour

Essay by kane_the_elitzUniversity, Bachelor'sA, December 2006

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Executive Summary

On 13th March 2004, Brigadier-General (NS) George Yeo, Trade and Industry Minister, announced in the Singapore Parliament that there is the possibility of a casino being allowed on Singapore's southern islands. After much deliberation, the Government's decision will finally be announced on the 18th April 2005. Our group is interested to find out about the reactions of Singaporeans to the idea of setting up a casino. Our project focuses on how the views of Singaporeans differ according to certain variables and demographics. For the context of our project, we explored how heavy gamblers react to the proposal, whether having children affect parents views on the opening of casino and the differences in views between the genders.

From our research and findings, we found out that 70.8% of Singaporeans buy 4D, Toto, engage in soccer betting and more. Of these, 40% of them spend more than S$100 on these activities on a monthly basis.

We also found out that 23.6% of Singaporeans who visited casinos spent more than S$300 per visit. We labeled this group of individuals as heavy gamblers.

Before conducting the survey, we assumed that more than 80% of heavy gamblers support the opening of the casino. Using that as a null hypothesis, we wanted to determine if the proportion of heavy gamblers that support the opening of the casino is less than 80%. We tested the claim at 5% level of significance. After conducting the survey, we conducted the hypothesis testing and found out that our sample statistic Z value is 2.44, which is greater than 1.645. We therefore reject the null hypothesis at 5% level of significance.

Through 95% confidence interval testing, we also know that the true population proportion of Singaporeans who support the opening of the casino lies between 50.05% and 68.74%.

Before we conducted the survey, we came up with the null hypothesis that more than 80% of the casino supporters are male. We are interested to test the relation that men are more likely to gamble and prefer the opening of the casino in Singapore. We tested the claim at 5% level of significance. After conducting the survey, we conducted the hypothesis testing and found out that the p-value of the Z value of our sample is 0.0823, which is greater than 0.05. There is insufficient evidence to reject the claim that more than 80% of casino supporters are males at 5% level of significance.

Before we conducted the survey, we came up with the null hypothesis that 80% of those who support the opening of a casino are those without children. We would like to challenge this assumption and hence did a hypothesis testing at 5% level of significance to prove that the proportion is not equal to 80%. We found out that our sample statistic Z value is -0.754, which is within the critical values of 1.96 and -1.96. We therefore conclude that is insufficient evidence to reject the claim that 80% of those who support the opening of a casino are those without children at 5% level of significance.

In view of the findings that we have gathered which shows support for the casino from the general public, together with the Government's seemingly pro-casino stand, we conclude that it is indeed likely that we will see one on our shores soon.

Issue of Concern

With the opening of casino in Singapore becoming more and more imminent, discussions and debates regarding the pros and cons of having a casino in Singapore is without doubt one of the hottest topics in town, making its way to newspaper headlines, countless forums and even television debate shows.

The debate arises because the magnitude of potential problems can prove to be disastrous. Singaporeans have raised several concerns on the possible building of the casino. Concerns include the increase in social evils such as increase in crime rate, family problems and resurfacing of underworld activities. Others worry about the erosion of values. Businessmen are skeptical of the impact of the casino on their business.

On the other hand, the government argues that there are also benefits that come along with the opening of casino. Prime Minister Lee Hsien Loong said, "Singapore must reinvent itself to remain attractive and competitive and building a casino is one of the possible ways to do it." He reassures that if one is built, the government will ensure there are systematic ways to cope with its social costs (The Straits Times, 20 March 2005).

Our group would like to tap on this opportunity to assess the receptivity of Singaporeans to the opening of the casino in our homeland. We are interested to find out possible reasons and characteristics that may cause the views to differ. In the context of our research, we would like to know how the views differ according to gender, whether having children affects parents views on the opening of casino and the extent to which heavy gamblers* support the opening of the casino.

*As to what constitutes heavy gamblers, please refer to Gamblers Support For Casino.

Sampling Method

To investigate our problem, we conducted a survey. In order to acquire an appropriate sample, we performed cluster sampling of all the districts in Singapore as each district is assumed to be representative of Singapore's population. After assigning numbers to the districts, 5 districts were selected using the random numbers table - Boon lay, Bishan, Woodlands, Telok Blangah, and Hougang. We went to the major shopping centre in each of the chosen districts since being in the district center, it is an area for convergence of people from all over the district. Targeting at 25 respondents per shopping centre, we conducted systematic random sampling at the entrances of each shopping centre over a weekend. Every respondent was separated by a 7-minute interval and had to be 21 years old and above since the proposed age restriction for the casino to be set up in Singapore is 21 years old.

Although we started out with a target sample size of 125, due to a non-response rate of 15.2% (19 out of 125), we only managed to garner 106 responses.

General Findings

Average Age of Respondents

Female28.1

Male32.8

Yes(%)No(%)

Number Of People Who Gamble7570.8%3129.2%

Do You Support Setting Up of Casino6359.4%4340.6%

Would You Gamble At A Singapore Casino7267.9%3432.1%

Average Spendings on Gambling Activities per Month< S$10S$10 to < S$50S$50 to < S$100S$100 to < S$150S$150 to < S$200> S$200

Frequency1018175619

Percentage13.3%24%22.7%6.7%8%25.3%

GAMBLERS SUPPORT FOR CASINO

Generally, we assume that people with a gambling nature would tend to exhibit support for the opening of the casino. With the higher stakes in casinos, heavy gamblers are more likely to be the ones patronizing them due to their higher expenditure in such activities.

We define heavy gamblers as those who spend more than S$100 on betting activities (4D, TOTO, etc) per month or those who spend more than S$300 per visit to a casino. People who fall into both categories are only counted once to prevent double counting.

Hypothesis Testing

Objective: To test the claim that at least 80% of the gamblers in Singapore will support the idea of setting up a casino in Singapore. A random sample of 106 Singaporeans was surveyed. Subsequently, 33 respondents fall under the category of heavy gamblers and out of which, 32 of them revealed that they support the idea of setting up a casino.

Let p be the population proportion of gamblers in Singapore who will support the idea of setting up a casino in Singapore. Sample proportion of gamblers out of a sample size of 106 is denoted by .

H0: p 0.8Population proportion of gamblers in Singapore will support the idea of setting up a casino in Singapore is at most 80%.

H1: p > 0.8Population proportion of gamblers in Singapore will support the idea of setting up a casino in Singapore is more than 80%.

Sample size n = 33 (gamblers)

Level of significance is given by α = 0.05

Critical Value = 1.645

Hypothesis Test for sample proportion (upper tail test)

Number of successes in sample refers to heavy gamblers who support the idea of setting up a casino in Singapore.

Since both np and n(1-p) are at least 5, can be approximated by a normal distribution with mean and standard deviation

As the sampling distribution of is approximately normal, we conduct an upper tail Z test for proportion in terms of number of heavy gamblers who support the idea of setting up a casino in Singapore.

Test Statistic:

Decision:

Since Z = 2.441 > 1.645, test statistic lies outside the acceptance region.

Thus, we reject the null hypothesis and conclude that there is insufficient evidence that at most 80% of the mean percentage of heavy gamblers support the idea of setting up a casino in Singapore at α = 0.05.

Confidence Interval

Objective: To form a 95% confidence interval for the true proportion of Singaporeans who support the idea of setting up a casino.

Sample size, n = 106

= proportion of sample who supports

= 63/106 = 0.594 or 59.4%

Confidence level: 95%

Z value = 1.96

Upper and lower confidence limits for the sample proportion:

Interpretation:

We are 95% confident that the true percentage of Singaporeans who support the idea of setting up a casino is between 50.05% and 68.74%

Although this range may or may not contain the true proportion, 95% of intervals formed from sample of size 106 in this manner will contain the true proportion.

As seen from the ongoing casino debate, Singaporeans having opposing views regarding this issue. Our findings revealed that a slightly larger proportion of our population is in support of the opening of a local casino.

Conditional Probabilities

Objective: To find out whether the probability that a Singaporean will support the setting up of casino and the probability that he/she is a gambler is statistically independent.

Support (S)Do not support (S')Total

Gamblers (G)32133

Non-gamblers (G')314273

Total 6343106

Pr (G) = 33 / 106

= 0.3113 or 31.13%

Pr (G') = 1 - 0.3113

=0.6887 or 68.87%

Test for Statistical Independence

Pr (S|G) = 0.9697

Pr(S) = 0.5943

Pr (S|G) ≠Pr(S),

Since Pr (S|G) ≠Pr(S), and Pr (S and G) ≠Pr (S) P (G), the probability that a Singaporean will support the setting up of casino and the probability that he/she is a gambler is not statistically independent. We can conclude that whether or not a person is a gambler affects if he/she supports the opening of a casino.

From our findings, the level of support for the setting up of a casino by heavy gamblers turned out to be higher than we expected. This could imply that if a casino is indeed set up in Singapore, it would attract a significant number of local gamblers, which might also translate into potential social problems in the future. This is the main concern of most Singaporean.

GENDER

In view of the fact that the general perception of the public involves a higher percentage of men being gamblers, our group is very interested to find out if there really is such a relation that men are more likely to gamble and feel more strongly for the setting up of the casino in Singapore. Hence, the other null hypothesis that our group wants to test is the claim that whether more than 80% of the casino supporters are male.

Hypothesis Testing using the P-value Test for Proportion

Let p be the population proportion of casino supporters who are male.

H0: p ≥0.8Population proportion of male casino supporters is greater than 80%

H1:p < 0.8 Population proportion of males is less than 80%

Sample size n = 63

Number of males in this sample = 46

Sample proportion ps = 46/63 = 0.73

Level of significance is given by α = 0.05

Critical Value = 1.645

From the normal table, the corresponding p-value is 0.0823 which is greater than the α value of 0.05 that we are testing at.

Hence, the value of p = 0.0823 and is within the acceptance region, we do not reject H0.

Conclusion: There is insufficient evidence to reject the claim that more than 80% of casino supporters are males at α = 0.05.

From this hypothesis testing, it could be seen that there is credibility in the claim that more than 80% of the casino supporters are males.

Furthermore, below are some of the survey results that our group obtained with respect to the gender divide. Earlier we have made a test to the claims that 73% of the casino supporters are males. From the side- to side bar chart below, it was observed that of the males and females surveyed, the support rate for males is about 71.9% as opposed to the female support rate of 40.5%.

This could be down to a few possible reasons that our group feel may have resulted in the findings that we have. Males in Singapore may generally be more excitement seeking and the opening of a casino could provide them with the excitement and fun that they crave.

The other reason could be that Singaporean females in general are still more conservative, and are more concerned about the potential social ills and moral issues that may arise from the setting up of the casino.

FAMILY'S EFFECT ON SUPPORT FOR CASINO

Objective: To investigate whether if a person has children or not affects his/her opinion towards the idea of a casino being opened in Singapore, and the extent of the influence.

Prior to the conducting of the survey, we hypothesized that 80% of those who support the opening of a casino are those without children. Having collected the results from our sample size, we now test our hypothesis using the Z Test for Proportion.

Hypothesis Testing

H0: p = 0.8Population proportion of casino supporters who have no children

H1: p ≠0.8Population proportion of casino supporters who have children

Sample size n = 63 (casino supporters)

No. of Successes X = 48

ps = X/n = No. of successes in the sample / sample size

= 48 / 63 = 0.762 (to 3 d.p.)

Level of significance is given by α = 0.05

Critical Values: ± 1.96

Test Statistic:

Decision: Do not reject H0 at α = 0.05.

Conclusion: There is insufficient evidence to reject the claim that 80% of those who support the opening of a casino are those without children.

Now let's look at it from another point of view.

From the side-by-side bar chart above, there are 2 observations.

Firstly, majority of people without children (78.7%) support the opening of a casino, as opposed to 21.3% against it. Secondly, majority of people with children (66.7%) are against the opening of a casino, as opposed to 33.3% for it.

From this, we can infer that people without children tend to show greater support towards the opening of a casino in Singapore as compared to people with children. This can perhaps be primarily due to the fact that people with children have more commitments to their families and have to shoulder more responsibilities. In addition, since gambling is commonly seen as a social ill, they would generally like to have an environment with less of such activities in which to bring up their children.

On the other hand, people without children are generally more carefree, with more time for personal pleasures, and are not tied down by so many family commitments.

Evaluation

Through our research and findings, we have gained a better understanding of the data by applying various statistical analysis methods.

However, we faced certain limitations. Due to the lack of information, we were unable to calculate the correlations between the different variables, which would have given us more interesting insights into the issue. Although we wanted to ensure higher precision, it is inappropriate to have open ended questions in our survey. Hence, most of the responses are categorized rather than numerical. This is a trade-off that is inevitable. In addition, our findings would have been more representative of the views of Singaporeans if we had a larger sample size. However, faced with time and manpower constrains, we had little choice but to settle for a sample size of 106.

THE END

APPENDIX B - Survey Form

Dear Respondent,

We are a group of students from National University of Singapore. We are conducting a survey to find out Singaporeans' views on the setting up of a Casino in Singapore. Please be assured that all information provided would be kept strictly confidential. We appreciate and thank you for your time and effort.

1.Do you bet on 4D, TOTO, Big Sweep, horse racing, soccer etc?

0 Yes0 No (Pls proceed to qn 3)

2.If yes, how much do you spend on these activities per month?

0 < S$10 0 S$10 to < S$50 0 S$50 to < S$100 0 S$100 to < S$150

0 S$150 to < S$200 0 > S$200

3.Have you ever visited a casino? (E.g. Genting Highland, Macau, cruises, underground casinos etc.)

0 Yes0 No (Pls proceed to qn 7)

4.How much do you spend per visit? (in S$)

0 < S$100 0 S$100 to < S$300 0 S$300 to < S$600 0 S$600 to < S$900

0 S$900 to < S$1200 0 > S$1200

5.Assuming a casino is being opened in Singapore which is able to satisfy all your needs and is of equal standard as overseas casinos, would you still visit overseas casinos?

0 Yes0 No

6.Would you support the idea of setting up a casino in Singapore?

0 Yes0 No

7.If a casino is opened in Singapore, would you visit it?

0 Yes0 No

8.What benefits do you think a casino would bring about? (Pls tick the 3 most important benefits to you)

0 Economic benefits/ Job creation

0 Boost tourism industry/ Attract more tourists

0 Provide a wider range of entertainment options

0 Divert local gamblers back to our own country

0 Put Singapore on an equal standing as other countries

0 Others : _______________________________________________________________

9.What problems do you think a casino would bring about? (Pls tick the 3 most important problems to you)

0 Potentially increase social ills ( Higher incidence of problem gambling,

increase in crime, etc)

0 Against Singapore pro-family policy

0 Has a cannibalizing effect on other local industries

0 Erodes our moral and religious values

0 Tarnishes Singapore's good reputation and image

0 Others : _______________________________________________________________

10.After looking at these benefits and problems, would you still support a casino being opened in Singapore?

0Yes0No

Demographics

Age 0 21 - 25 0 26 - 30 0 31 - 35 0 36 - 40 0 41 - 45 0 46 - 50 0 51- 55

0 56 - 60 0Others: _________

Gender: F / M

Marital Status: Single / Married

No. of children 0 0 0 1 0 2 0 3 0 4 0 >4

Income Level 0 S$0 to < S$1,000 0 S$1,000 to < S$2,000 0 S$2, 000 to < S$3,000

0 S$3,000 to < S$4,000 0 > S$4,000

Occupation

0 Student 0 Executive/Senior management 0 Professional 0 Educational/Training

0 General 0 administrative/supervisory 0 Sales/Marketing/Advertising

0Others:_____________

Thank you