Reference no: EM132672293
Question 1 Random Sampling
(i) In 2020, UTS has 50,000 students. We now assign numbers from 1 to 50,000 as ID numbers to these students. Please use the following numbers from Random Number Book to draw a random sample of 6 students from them. Please write down the six ID numbers and the process that you draw your sample.
• 00000 10097 32533 76520 13586 34673 54876 80959 09117 39292 74945
• 00001 37542 04805 64894 74296 24805 24037 20636 10402 00822 91665
• 00002 08422 68953 19645 09303 23209 02560 15953 34764 35080 33606
• 00003 99019 02529 09376 70715 38311 31165 88676 74397 04436 27659
• 00004 12807 99970 80157 36147 64032 36653 98951 16877 12171 76833
(ii) Now we know that these six students' ages are 18, 25, 30, 28, 34 and 22. Please calculate the mean, variance and standard deviation of their ages.
Question 2 Sample Size
You are requested to design a survey of households, designed to measure the key variable (among others) of travel time per day (minutes) for each person. You are asked to collect sufficient data to permit you to estimate the average travel time per person to within ±5 percent at 90% confidence. From previous studies, you estimate that the average daily travel time per person per day is 80 minutes, and the variance in this statistic is 5245. The population of households from which the sample is to be drawn is 5 million.
(i) What sample size would you require to achieve this level of accuracy?
(ii) Suppose that your client states that this sample size is too large for the budget. As an alternative, you propose to post stratify the sample by household size. From the census, you have the information shown in Table 1 below about the number of households by household size, and your prior information about the variance of average travel time per person per day by household size is also shown in the table.
(a) If your sample size remains the same as the result from question (a), calculate the weights for each stratum and also calculate the variance and standard error of the mean after post-stratified sampling is applied.
(b) Based on this result, explain why post stratified sampling can reduce sample size if same level of survey accuracy is required.
Table 1 Information of number of household by household size
|
Household Size
|
Population
|
Estimated Variance
|
|
1
|
1,200,000
|
602
|
|
2
|
1,910,000
|
2,400
|
|
3
|
900,000
|
3,790
|
|
4
|
600,000
|
6,450
|
|
5+
|
390,000
|
9,200
|
(iii) If the population was 10,000, what would the sample size be? What is the minimum population size that you think would be justified to ignore the finite population correction factor? Show by calculation how you justify this.
Question 3 Response Rate
In a two-stage survey, you started out by listing 10,000 telephone numbers to be used for the initial recruitment calls. Of these, you ended up using 8,500. 3,600 households were successfully recruited. All of the telephone numbers were attempted. The results of the attempts are shown in Table 2. In the second stage, you sent out a package with questionnaires by mail to respondents and asked them to return their response. You received back in the post 2,900 survey packages. 50 packages were returned by the Post Office as being undeliverable. After opening and inspecting these, 60 were found to be blank, while a further 240 were rejected as being too incomplete to use. What is the first stage response rate and also the second stage response rate? What is the overall response rate?
Table 2 Results of attempts in telephone recruitment
|
Refusals
|
Terminations
|
Busy/No Answer
|
Requests for call back that were not completed
|
Disconnected
|
Not in Service
|
Number changed
|
Non- Residential
|
Fax/ Modem
|
No Eligible HH Members
|
|
1980
|
298
|
614
|
290
|
98
|
278
|
59
|
973
|
21
|
289
|
Question 4: Trave Diary Design
UTS is planning to conduct a travel survey for residents living in the City of Sydney. Face-to-face interview will be utilised for the survey. Please design a household travel survey "diary" to collect travel information from the respondents.
Diary should include:
- Travel information (start and end time, travel mode, vehicle occupancy (if by car))
- Activity information (location, type of activity or trip purpose)
You can only write one trip and one activity as an example (the box below is the session you need to complete).
In a real survey, you can assume one can make more than 10 trips/activities per day. So you will repeat this session/page for more than 10 times in the diary.
Start your diary with:
Trip 1 and activity 1:
1. Where were you at 4:00 am
a. Travelling - Go to Question xxx
b. At a place - Go to Question 2
2. Where is this?
Address:
Trip 2 and activity 2
1. when did you arrive there
2. Where is this
...
Trip 3 and activity 3
1. when did you arrive there
2. Where is this
...
...
Attachment:- Assignment 3 for Subject.rar