Stratified Sampling

Question 1. (travel agency) 

  1. Target population: People aged 20-65 years.

We can draw a sample of 1000 persons using Stratified sampling. The stratification is done as follows:

  • <15years
  • 15-25 years
  • 26-60 years
  • >60 years

Also it’s possible to do stratification on basis of travel destination, amount to be spent or mode of booking holiday etc.

  1. We would email the survey to the persons using email-marketing software’s or online platforms (like Survey monkey etc.). We would also send it to them through ordinary mail of their residence or office.
  1. Pilot survey: It would be conducted at 15 different tourist spots. We can choose 50 persons for pilot survey. We can also estimate the non-response rate from this pilot survey. We would fill survey from them either at the sport or call them to office and give them 40 min to complete it.
  1. https://www.airbnb.co.in/

https://www.trivago.in/

https://www.surveymonkey.com/

  • Cover letter of Questionnaire

The questionnaire is made for helping travel agent in understanding the customers. The travel agency is a planning to make its business strategy for next 3 years. The company has planned to conduct a survey by questionnaire. The objective of questionnaire is to know the taste of travellers that includes expenditure, favorite destination, length of stay, accommodation preference of customers.

The information will highlight the likes and dislikes of customer and help travel agency in making a good strategy for future. 

Questionnaire for travel agency 

Please respond to the following questions.

Please provide appropriate responses to the following questions . No part of this survey will be made public/be used for prosecution purposes . The information collected would be kept private .

Name: ________________

Age: ______

Todays date ________________

Address ________________ ________________ ________________ ________________ ________________

Date of birth ________________

Sex:     ☐Male☐ Female

TRAVEL PREFERENCE

 

  1. What is your age
  • <15
  • 15-25
  • 26-60
  • >60
  1. Have you ever gone on a trip with a travel agency?
  • Yes
  • No
  1. How often do you go on a trip? (Please tick only 1)
  • rarely
  • sometimes
  • often
  1. For how many days do you prefer to travel? (Please tick only 1)
  • 1-4
  • 5-10
  • 8-20
  • 21-35
  1. Which travel destinations are popular to you (tick all that apply)?
  • Domestic
  • Asia
  • Europe
  • North & South America
  • Africa
  • Others
  1. With how many people do you travel frequently? (Please tick only 1)
  • Alone
  • 1-3
  • 4-10
  • more than 10
  1. Which, according to you, is the issue concerned while planning for travelling?
  • Security and safety
  • Traditional norms and beliefs
  • Tickets management
  • other
  1. How do you book your holiday mostly? (Please tick only 1)
  • Personally
  • Through a travel agent
  • Online
  1. How much do you wish to spend on a trip (per person)?
  • <$500
  • $500-1000
  • $1001-1500
  • >$1501
  1. Which among the following is the most preferred time for travelling?
  • Christmas vacations
  • Summer vacations
  • Off-season

OCCUPATION & INCOME:

  1. What’s your occupation? _________________
  2. Do you travel at least once a year for business/conference?
  • Yes
  • No
  1. What’s your annual income?
  • $10000-50000
  • $50,001-100,000
  • $100,001-200,000
  • $200,001-500000

PREFERENCES:

  1. How has been your experience with travel agencies? (1 for extremely bad, 2 for bad, 3 for average, 4 for good, 5 for extremely good)
  • 1
  • 2
  • 3
  • 4
  • 5
  1. What kind of accommodation do you prefer? (Please tick only 1)
  • 3 star hotels
  • 4 star
  • private villa
  • 7 star
  1. Which type of tourist spots do you like? (Tick all that apply)
  • Historical
  • Entertainment
  • Natural beauty
  • Other (please specify)___________________
  1. Are you interested in adventure spots? __________ (Y/N)

INSURANCE& MEMBERSHIP

  1. Do you possess travel insurance? ___________ (Y/N)
  2. Do you possess any travel club membership?_______(Y/N)
  3. Does your company/any other organization/Government sponsor your tours? ________________ (Y/N)

Question 2 (drug addict) 

  1. Population & Sampling :

Most drug addicts would be between the age of 13-45 years (assumption)  . The administration would have a list of all such persons. We’ll consider them as the population.

Then we can further subdivide them into groups , like <15 years , 15-20 years , 21-50 years and >50 years. We may also form the stratification according to income or education .

We can perform usual stratified sampling techniques on this population using R/Matlab and choose around 1000 individuals ( total) for our study .

  1. Since the data being collective is sensitive in nature , we must assure the respondents that their privacy would be protected and they won’t get into legal trouble. We can email them the questionnaires or mail it to them through ordinary mail . For students , we can go to the school/college/institution and ask them to participate in the survey ( with support from the authorities). This would lower the non-response rate for students .
  2. We would conduct pilot survey by distributing questionaires to drug agencies. So the drug addicts will fill it. We’ll aim to draw a sample of 30 people using the stratified sampling technique.
  3. Sites used: https://www.dea.gov/index.shtml

https://www.surveymonkey.com/.

  • Cover letter:

This questionairre is related to the drug adddicts of society. It is divided into different sections like background, medical history, symptoms etc. the target audience are drug addicts. The objective behind this questionaireis  developing policy for restraining drug addiction & spread awareness about drug abuse. 

Questionnaire for gathering INFORMATION REGARDING DRUG ADDICTION 

Please provide appropriate responses to the following questions . No part of this survey will be made public/be used for prosecution purposes . The information collected would be kept private .

Name: ________________

Age: ______

Occupation :___________________

Todays date ________________

Address ________________ ________________ ________________ ________________ ________________

Date of birth ________________

Sex:     ☐Male☐ Female

BACKGROUND

  1. What is your age
  • <15
  • 15-20
  • 21-50
  • >50
  1. What is your origin
  • white
  • black
  • Asian
  • African
  • american 
  1. Annual Family income : (Please tick only 1)
  • < $20,000
  • $20,000-40,000
  • $40,001-70,000
  • >$70,001
  1. Highest level of education : (Please tick only 1)
  • Primary school
  • Middle school
  • High school
  • Graduate
  • Masters or higher
  • Not educated
  1. If you’re a student or < 25 years old ,Please mark this :

Highest level of education of father :(Please tick only 1)

  • Primary school
  • Middle school
  • High school
  • Graduate
  • Masters or higher
  • Not educated

ADDICTION HISTORY & SYMPTOMS

  1. Have you ever used drugs? _______________________ ( Answer in Y/N)
  2. Is there any history of drug addiction/alcohol addiction in your family ? __________________________________ ( Answer in Y/N)
  3. If answer of 4 is yes then how were you first introduced to drugs (tick only 1)
  • through friends
  • Tried yourself
  • Through relatives
  • Through dealer
  • Others
  1. How much do you spend on drugs monthly
  • <$100
  • $100_500
  • $501-2000
  • >$2000
  1. How frequently do you use drugs? (Please tick only 1)
  • Regularly
  • Once in a while
  • Very rarely
  1. Have you observed any of these symptoms in your body ? (Please tick ALL RELEVANT RESPONSES)
  •  
  • Dilated pupils
  • Chills and sweating.
  • Involuntary shaking (tremors)
  • Muscle cramping and teeth clenching
  • Other (please specify)___________________
  1. If you’ve ticked any responses in Q.11, Have you consulted a doctor ? ______________________ ( Y/N)
  1. If you’re a student , is there any medical cell in your school/college to control drug addiction ? ________________ (Y/N)

MEDICAL HISTORY :

  1. Do you suffer from depression ? ________________ (Y/N)
  1. If you answered yes to Q.12 , Please rate it on aa scale of 1 to 4 (1 for minor depression, 2 for moderate depression , 3 for quite a bit, 4 acute depression)
  • 1
  • 2
  • 3
  • 4
  1. How often do you go through a health check-up? (Please tick only 1)
  • Less than once a year
  • Twice a year
  • More than twice a year
  1. If your answer to Q.15 is yes , then which drug/drugs were it ? (Please tick ALL RELEVANT RESPONSES)
  • Heroin
  • Cocaine
  • Marijuana
  • Lsd
  • Meth
  • Other (please specify)___________________
  1. What makes you addicted towards drugs?
  • Stress
  • Money issues
  • Depression
  • Family issues
  • Any other issues
  1. Do you need any help regarding rehab to stop the addiction ? ____________ (Y/N)

Solution 

TRAVEL

The aim of the report is to provide summary of the travel data and answer the question whether there is significant association between the age of the respondents and the amount spent on a travel. Moreover, it also answers the question whether age is a driver in the selection of popular destination. The sample data used for the analysis consists of 200 observations over 31 questions.

According to the results the majority of the respondents are aged 26-60 years (40.5%), followed by the group of 15-25 years of age (23%).  The distribution of age is skewed to the left (Appendix A.2) with high concentration of observations in the higher age range.

The majority of the respondents prefer Christmas vacations as the best time to travel (44%) and another 40% prefer the off season.

The majority of the sample (44.5%) have an annual income between $50 001 and $ 100 000 and the second large group, 29% of the sample have income between $100 001 and $200 000. Most of the people in the sample only travel sometimes (40.5%) while 39% travel often and 20.5% travel rarely.

Usually the days of travel are between 9 and 20 days (37% of the sample) and rarely above 21 days (18% of the sample.

Only 23.5% of the respondents travel alone, 38% travel accompanied by 1 to 3 people, 23% travel with 4 to 10 people and just 15.5% travel with more than 10 people.

Most of the respondents book their trip either with a travel agent or online, a total of 80% of the sample. However, there are still 20% who are booking their trip personally.

The amount of money they spent is on average between $1001 and $1500 (36% of the sample), rarely below $500 (18% of the sample). The distribution of the amount of money spent is skewed to the left with concentration of observations in the higher amount range.

According to the Chi-square test used (Appendix A.1) to determine whether there is significant association between the age and the money spent the null hypothesis there is no association cannot be rejected at the 5% significance level (Chi-square (9) = 5.965 with p-value = .743).

Therefore the conclusion is that there is no significant association between age and amount of money spent on a travel. However, in further analysis more sophisticated ways of analysis such as regression could be conducted to account for the influence of other factors as well and to determine the direction of relationship.

The respondents who prefer to go on Christmas vacations (44% of the total sample) mostly visit Africa (20.5% of the total sample). Those who go on summer vacations (16% of the total sample) also mostly visit Africa and 13.5% of the participants are off-season travelers going to Africa. Only 3.5% chose non-popular destinations for their Christmas vacations and just as many go to Domestic popular destinations during their Christmas trip. The second most visited destination amongst the summer travelers is Europe. North & South America is the second most preferred off season popular destination.

Finally, according to the multinomial regression output the following conclusion can be made about age as the driver of popular destinations. 9% of the participants haven’t gone to any popular destination, 7% have each gone to Domestic popular destinations and to Asian popular destinations, 17% have gone to European popular destinations, 20.5% to popular destinations in North & South America and 39.5% to African popular destinations. However, the Chi-square test (15.863 with p-value = .391) shows age has no significant effect on the popular destinations. In other words, the choice of popular destination is not affected by the age of the person.

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Drugs 

The aim of the report is to provide summary of the drugs data. The sample data used for the analysis consists of 225 observations over 29 questions.

According to the results the majority of the respondents are above 50 years (42.7%), 24.4% are aged between 21 and 50 years and there are only 15.6% below 15 years of age.

Nearly half of the sample participants use drugs once in a while (49.3%), 12.9% use drugs ver rarely and 37.8% use them regularly.

There is no participant without depression, nearly 80% of the sample either have moderate or quite a bit of depression. Only 14.7% have minor depression.

At the same time nearly half of the sample (44.9%) performs health check ups less than once a year and only 12.9% go to health check ups more than twice a year.

The reasons for addiction are various. 23.1% have family issues, for 22.7% of the sample the reason is the depression, for 19.6% it is due to stress, for 17.3% the reason is money issues.

None of the respondents declared they need help to stop addition and at the same time 100% of the sample have tried drugs.

The origin of the participants is various: nearly equal parts white, black, Asian, African, and American.

Most of the sample participants declare family annual income to be between $40 001 and $70 000 (42.7%).

There is no high concentration in any type of education – nearly equal parts of the participants have middle school, masters or higher (around 22%). There is smaller proportion (15.1%) without education and 23.1% with high school.

The majority of the sample have masters or higher for education of the father (39.1%), 27.6% have their father graduate. For the majority there is drug addiction in the family (62.7%).

Most of the sample (40.4%) have introduced themselves to drugs while 23.6% were introduced by a friend and 20.9% by some dealer.

Most of the participants spend between $501 and $2000 for drugs monthly (38.2%) and another 37.3% spend between $100 and $500 monthly. 24.4% spend more than $2000.

According to the several cross-tabs performed and the Chi-square test statistics the following conclusions can be made. Age is not significantly associated with the monthly expenditure on drugs (Chi-square = 6.536 with p-value = 0.366). Age is not significantly associated with frequency of drug usage (Chi-square = 7.177 with p-value = 0.305). Age is not significantly associated with annual family income (Chi-square = 5.579 with p-value = 0.781). Age is not significantly associated with the way the person was introduced to drugs (Chi-square = 6.497 with p-value = 0.689).

Finally, according to the multinomial regression output the following conclusion can be made about origin as the driver of monthly drug expenditure. The origin is not a significant driver of the monthly drug expenditure (Chi-square = 4.915 with p-value = .767).

 Appendix A. Travel data

A.1.1

Frequency Tables

age of respondents 
 FrequencyPercentValid PercentCumulative Percent 
Valid<154020.020.020.0 
15-254623.023.043.0 
26-608140.540.583.5 
>603316.516.5100.0 
Total200100.0100.0  
preferred time of travel
 FrequencyPercentValid PercentCumulative Percent
ValidChristmas vacations8844.044.044.0
summer vacations3216.016.060.0
off season8040.040.0100.0
Total200100.0100.0 
annual income 
 FrequencyPercentValid PercentCumulative Percent 
Valid$10000-$500002311.511.511.5 
$50001-$1000008944.544.556.0 
$100001-$2000005829.029.085.0 
$200001-$5000003015.015.0100.0 
Total200100.0100.0  
                
number of trips 
 FrequencyPercentValid PercentCumulative Percent 
Validrarely4120.520.520.5 
sometimes8140.540.561.0 
often7839.039.0100.0 
Total200100.0100.0  
days of travel 
 FrequencyPercentValid PercentCumulative Percent 
Valid1- 44522.522.522.5 
5-104522.522.545.0 
9-207437.037.082.0 
21-353618.018.0100.0 
Total200100.0100.0  
no of ppl who accompany you
 FrequencyPercentValid PercentCumulative Percent
ValidAlone4723.523.523.5
1-37638.038.061.5
4-104623.023.084.5
more than 103115.515.5100.0
Total200100.0100.0 
                
way of booking
 FrequencyPercentValid PercentCumulative Percent
ValidPersonally4020.020.020.0
through a travel agent8040.040.060.0
Online8040.040.0100.0
Total200100.0100.0 
amount of money to be spend 
 FrequencyPercentValid PercentCumulative Percent 
Valid<$5003618.018.018.0 
$501-$10004422.022.040.0 
$1001-$15007236.036.076.0 
>$15004824.024.0100.0 
Total200100.0100.0  
           

 

A.1.2

The Chi-square test used to test association between two categorical variables: age of the respondents and amount of money to be spent.

Chi-Square Tests
 ValuedfAsymptotic Significance (2-sided)
Pearson Chi-Square5.965a9.743
Likelihood Ratio6.1249.727
Linear-by-Linear Association.0921.762
N of Valid Cases200  
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 5.94.
age of respondents * amount of money to be spend Crosstabulation
 amount of money to be spendTotal
<$500$501-$1000$1001-$1500>$1500
age of respondents<15Count95141240
Expected Count7.28.814.49.640.0
15-25Count81416846
Expected Count8.310.116.611.046.0
26-60Count1419282081
Expected Count14.617.829.219.481.0
>60Count5614833
Expected Count5.97.311.97.933.0
TotalCount36447248200
Expected Count36.044.072.048.0200.0

 

A.1.3

Multinomial regression

The multinomial regression is used because the dependent variable is nominal with 6 categories, popular destinations. The independent variable is a categorical variable with 4 levels.

Case Processing Summary
 NMarginal Percentage
popular_destinationsnone189.0%
Domestic147.0%
Asia147.0%
Europe3417.0%
North & South America4120.5%
Africa7939.5%
age of respondents<154020.0%
15-254623.0%
26-608140.5%
>603316.5%
Valid200100.0%
Missing0 
Total200 
Subpopulation4 
Model Fitting Information
ModelModel Fitting CriteriaLikelihood Ratio Tests
-2 Log LikelihoodChi-SquaredfSig.
Intercept Only79.585   
Final63.72215.86315.391

 

A.1.4.

The crosstab is used to compare two nominal variables: preferred time of travel and popular destinations.

preferred time of travel * popular_destinationsCrosstabulation
 popular_destinationsTotal
noneDomesticAsiaEuropeNorth & South AmericaAfrica
preferred time of travelChristmas vacationsCount77614134188
% of Total3.5%3.5%3.0%7.0%6.5%20.5%44.0%
summer vacationsCount132961132
% of Total0.5%1.5%1.0%4.5%3.0%5.5%16.0%
off seasonCount104611222780
% of Total5.0%2.0%3.0%5.5%11.0%13.5%40.0%
TotalCount181414344179200
% of Total9.0%7.0%7.0%17.0%20.5%39.5%100.0%

A.2. Descriptive figures

A.2.1 Plots of Age of respondents

A.2.2 Plots of Age of preferred time of travel

A.2.3 Plots of annual income

A.2.4 Plots of Number of trips

A.2.5 Plots of Days of travel

A.2.6 Plots of Number of people accompanying you

A.2.7 Plots of Way of booking

A.2.8 Plots of Amount of money to be spent

 Appendix B. Drugs data

B.1.1

Frequency Table

age of respondents 
 FrequencyPercentValid PercentCumulative Percent 
Valid<153515.615.615.6 
15-203917.317.332.9 
21-505524.424.457.3 
>509642.742.7100.0 
Total225100.0100.0  
frequency of drug usage 
 FrequencyPercentValid PercentCumulative Percent 
Validregularly8537.837.837.8 
once in a while11149.349.387.1 
very rarely2912.912.9100.0 
Total225100.0100.0  
rate depression 
 FrequencyPercentValid PercentCumulative Percent 
Validminor depression3314.714.714.7 
moderate depression8839.139.153.8 
quite a bit8738.738.792.4 
acute depression177.67.6100.0 
Total225100.0100.0  
health check up
 FrequencyPercentValid PercentCumulative Percent
Validless than once a year10144.944.944.9
twice a year9542.242.287.1
more than twice a year2912.912.9100.0
Total225100.0100.0 
                     

 

 

reason of addiction
 FrequencyPercentValid PercentCumulative Percent
Validstress4419.619.619.6
money issues3917.317.336.9
depression5122.722.759.6
family issues5223.123.182.7
any other issues3917.317.3100.0
Total225100.0100.0 
need help to stop addiction 
 FrequencyPercentValid PercentCumulative Percent 
Validno225100.0100.0100.0 
Your origin? 
 FrequencyPercentValid PercentCumulative Percent 
Validwhite4118.218.218.2 
black4520.020.038.2 
asian5223.123.161.3 
african4319.119.180.4 
american4419.619.6100.0 
Total225100.0100.0  
                

 

 

annual family income 
 FrequencyPercentValid PercentCumulative Percent 
Valid<$200004821.321.321.3 
$20000-400004017.817.839.1 
$40001-700009642.742.781.8 
>$700004118.218.2100.0 
Total225100.0100.0  
education
 FrequencyPercentValid PercentCumulative Percent
Validnot educated3415.115.115.1
middle school5022.222.237.3
high school5223.123.160.4
graduate3917.317.377.8
masters or higher5022.222.2100.0
Total225100.0100.0 
education of father
 FrequencyPercentValid PercentCumulative Percent
Validmiddle school3214.214.214.2
high school4319.119.133.3
graduate6227.627.660.9
masters or higher8839.139.1100.0
Total225100.0100.0 
           

 

tried drugs 
 FrequencyPercentValid PercentCumulative Percent 
Validyes225100.0100.0100.0 
drug addiction in family 
 FrequencyPercentValid PercentCumulative Percent 
Validno8437.337.337.3 
yes14162.762.7100.0 
Total225100.0100.0  
how you got introduced to drugs
 FrequencyPercentValid PercentCumulative Percent
Validby friend5323.623.623.6
yourself9140.440.464.0
some dealer4720.920.984.9
other3415.115.1100.0
Total225100.0100.0 
expenditure on drugs monthly 
 FrequencyPercentValid PercentCumulative Percent 
Valid100-5008437.337.337.3 
501-20008638.238.275.6 
>20005524.424.4100.0 
Total225100.0100.0  
                

B.1.2

Crosstabs are used to compare the 4 age groups against several characteristics: monthly expenditure on drugs, frequency of drug usage, annual family income and way of introduction to drugs.

age of respondents * expenditure on drugs monthly Crosstabulation
Count
 expenditure on drugs monthlyTotal
100-500501-2000>2000
age of respondents<1512111235
15-201912839
21-5023211155
>5030422496
Total848655225
Chi-Square Tests
 ValuedfAsymptotic Significance (2-sided)
Pearson Chi-Square6.536a6.366
Likelihood Ratio6.3866.381
Linear-by-Linear Association.0671.796
N of Valid Cases225  
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 8.56.
age of respondents * frequency of drug usage Crosstabulation
Count
 frequency of drug usageTotal
regularlyonce in a whilevery rarely
age of respondents<151715335
15-201124439
21-502524655
>5032481696
Total8511129225
Chi-Square Tests
 ValuedfAsymptotic Significance (2-sided)
Pearson Chi-Square7.177a6.305
Likelihood Ratio7.0926.312
Linear-by-Linear Association2.0291.154
N of Valid Cases225  
a. 1 cells (8.3%) have expected count less than 5. The minimum expected count is 4.51.
age of respondents * annual family income Crosstabulation
Count
 annual family incomeTotal
<$20000$20000-40000$40001-70000>$70000
age of respondents<1510413835
15-208816739
21-50107281055
>502021391696
Total48409641225
Chi-Square Tests
 ValuedfAsymptotic Significance (2-sided)
Pearson Chi-Square5.579a9.781
Likelihood Ratio5.5779.781
Linear-by-Linear Association.0081.930
N of Valid Cases225  
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 6.22.
age of respondents * how you got introduced to drugs Crosstabulation
Count
 how you got introduced to drugsTotal
by friendyourselfsome dealerother
age of respondents<159128635
15-209138939
21-50122514455
>502341171596
Total53914734225
Chi-Square Tests
 ValuedfAsymptotic Significance (2-sided)
Pearson Chi-Square6.497a9.689
Likelihood Ratio6.8199.656
Linear-by-Linear Association.4861.486
N of Valid Cases225  
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 5.29.

B.1.3

Multinomial regression is used because the dependent variable is nominal with 4 categories and the independent variable is also a nominal variable with 5 categories.

Case Processing Summary
 NMarginal Percentage
expenditure on drugs monthly100-5008437.3%
501-20008638.2%
>20005524.4%
your origin?white4118.2%
black4520.0%
asian5223.1%
african4319.1%
american4419.6%
Valid225100.0%
Missing0 
Total225 
Subpopulation5 
Model Fitting Information
ModelModel Fitting CriteriaLikelihood Ratio Tests
-2 Log LikelihoodChi-SquaredfSig.
Intercept Only44.517   
Final39.6034.9158.767

 

B.2. Descriptive figures 

B.2.1. Plots of age of respondents

B.2.1. Plots of frequency of drug usage

B.2.1. Plots of age of respondents

B.2.3. Plots of rate of depression

B.2.4. Plots of health check up

B.2.5. Plots of age of reason of addiction

B.2.6. Plots of need help to stop addiction

B.2.7. Plots of Origin

B.2.8. Plots of annual family income

B.2.9. Plots of Education

B.2.10. Plots of Education of father

B.2.11. Plots of tried drugs

B.2.12. Plots of drug addiction in family

B.2.13. Plots of How you got introduced to drugs

B.2.14. Plots of Expenditure on drugs monthly

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/BAR(SIMPLE)=COUNT BY Q4.

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/BAR(SIMPLE)=COUNT BY Q5.

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/BAR(SIMPLE)=COUNT BY Q6.

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/BAR(SIMPLE)=COUNT BY Q7.

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/BAR(SIMPLE)=COUNT BY Q8.

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/BAR(SIMPLE)=COUNT BY Q9.

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