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STATS 101/108 - Chapter 6 Quantification | Whakamehua: Task
Introduction
Why do people visit Aotearoa New Zealand? The Ministry of Business, Employment and Innovation (BMEI) regularly carries out the International Visitor Survey (IVS), a survey of a random sample of visitors to New Zealand, to answer this and related questions. Information about the survey can be found on the BMEI website.
Watch this brief video for why one YouYuber thinks people should visit Aotearoa New Zealand.
In this task, we will use survey data from di"erent groups of people to explore how human observations and experiences can be quantified.
Q1
For this question, you need to compare two appropriate sample proportions.
Head to the International visitors app. Select di"erent variables and familiarise yourself with the visualisations.
The app allows you to visualise data from the latest iteration of the IVS as stacked bar charts. Based on the selection of the first variable, a table of the totals is provided, and for each of the other variables the survey question is given together with the visualisation.
The app has data for five categorical variables:
airport : the airport where a visitor entered Aoetearoa New Zealand (Auckland, Christchurch, Queenstown, Wellington)
age_range : the age group of a visitor (Under 20, 20 - 29, 30 - 39, 40 - 49, 50 - 59, 60 or older, Rather not say)
country_of_residence : the world region in which the visitor lives (Africa and Middle East, Americas, Asia, Europe and UK, Oceania)
purpose_of_visit : the main reason for the visitor to come to Aotearoa New Zealand (Business, Holiday / vacation, Other, Visiting friends / relatives)
gender : the gender of the visitor (Another Gender, Female, Male, Rather not say)
The purpose of this investigation is to find out why different groups of people visit Aotearoa New Zealand.
Select a variable in the drop-down menu to determine which groups you are planning to compare. This variable must be one of: airport , age_range, country_of_residence or gender . Write down this variable.
Identify two levels within your chosen variable that you are going to compare. In the app the two levels are represented by two stacked bars in one of the charts. Write down the two levels and the number of responses for each level. Hint: the number of responses are given on the top of the app when the variable is selected.
For example, if there was a variable called birth month , you may want to decide to compare the levels “January” and “October” and copy the number of responses from the table.
The response variable for your investigation is purpose_of_visit . Take a screenshot of the plot in the app that shows the purpose_of_visit for your selected variable.
Select one level of purpose_of_visit to focus on for your investigation and write it down. This could be Business, Holiday/vacation, Other or Visiting friends/relatives. Make sure you select a level that you are interested in.
For each of the two groups you are comparing, write down the proportions that are the level you are interested in. Hint: On a laptop/computer, you can see the proportion by hovering over the relevant part of the bar chart in the app. On a tablet, you need to click on the relevant part of the plot.
The overall research question for this task is “How does the proportion of all international visitors in the [group 1 description] group that come to Aotearoa New Zealand for [level of purpose_of_visit ] compare to the proportion of all international visitors in the [group 2 description] group that come to Aotearoa New Zealand for [level of purpose_of_visit ]?”
Write down which of the two groups has the higher proportion of the level you are investigating.
Construct your answer using the following structure. Copy and paste it into the template and complete your answers accordingly.
The variable for the investigation:
The level of group 1 and the number of respondents:
The level of group 2 and the number of respondents:
The screenshot of the plot:
The level of purpose_of_visit you are investigating:
The proportion of the level for group 1:
The proportion of the level for group 2:
The group with the higher sample proportion:
Q2
For this question, you need to construct an appropriate confidence interval for a di"erence in proportions.
Copy the level of purpose_of_visit that you selected in Q1.
Use the confidence interval calculator linked in the coursebook to construct a confidence interval for the difference in proportions of your purpose_of_visit between the two groups you selected in Q1. You will have to decide on the correct sampling situation.
Take a screenshot of the confidence interval calculator that shows the data entered and the confidence interval.
Write one sentence explaining why you chose the sampling situation that you did.
Construct your answer using the following structure. Copy and paste it into the template and complete your answers accordingly.
The level of purpose_of_visit you are investigating (from Q1):
The screenshot of the confidence interval calculator:
One sentence explaining why you chose the sampling situation:
Q3
For this question, you need to interpret a confidence interval for a di"erence in proportions in terms of a comparison.
Copy the confidence interval from Q2 as it is shown in the confidence interval calculator.
Write one sentence that interprets the confidence interval for di"erence in proportions in terms of a comparison. Note: The research question was provided in Q1, and your interpretation should clearly answer this research question.
Construct your answer using the following structure. Copy and paste it into the template and complete your answers accordingly.
The confidence interval from Q2:
The interpretation of the confidence interval:
Q4
For this question, you need to evaluate a claim by considering whether it is supported by a confidence interval.
Copy the confidence interval from Q2.
Write down the name of the group you identified as having the higher sample proportion in Q1.
Write one sentence evaluating a claim that “The proportion of all international visitors in the [description of group] group that come to Aotearoa New Zealand for the purpose of [level of purpose_of_visit ] is higher than that of the [description of the other group] group” by considering whether it is supported by the confidence interval.
Construct your answer using the following structure. Copy and paste it into the template and complete your answers accordingly.
The confidence interval from Q2:
The group with the higher sample proportion from Q1:
One sentence evaluation of whether the claim can be made:
Q5
For this question, you need to contrast di"erent survey questions.
In this chapter, you learned how human observations and experiences can be quantified. The survey question in the IVS was: “What was your main reason for your trip to New Zealand?”. Think about another way to ask visitors about reasons for their trip to Aotearoa New Zealand. I.e., do not just paraphrase the above question — come up with a new question. Write it down.
It may help to consider the five main types of survey questions we focussed on in Chapter 6 of the coursebook.
Explain ONE advantage and ONE disadvantage of this differently worded question compared to the one used in the survey.
Construct your answer using the following structure. Copy and paste it into the template and complete your answers accordingly.
A new survey question about trip reasons:
One advantage:
One disadvantage:
Q6
For this question, you need to reflect on the learning focus for this chapter (Quantification).
Describe in your own words ONE important idea from this topic. Do not just copy one of the learning objectives or something from the notes or other learning resources. One sentence is enough, but you must write about your own personal reflection.
Construct your answer using the following structure. Copy and paste it into the template and complete your answers accordingly.