8.6 Optional questions
These questions are optional; e.g., if you need more practice, or you are studying for the exam. (Answers are available in Sect. A.8.)
8.6.2 Optional: CI for differences between means
This question has a video solution in the online book, so you can hear and see the solution.
In 2011, Eagle Boy's Pizza ran a campaign (Dunn 2012) that claimed that Eagle Boy's pizzas were larger than Domino's large pizzas. Eagle Boy's made the data behind the campaign publicly available.
Each sample contained similar pizzas types (the three toppings were: supreme, Hawaiian, meat-lovers; the three base types were deep, thin, mid).
Some output from a sample of \(125\) of Eagle Boys' and Domino's large pizzas is shown in Fig.
8.9 (jamovi) and Fig. 8.10 (SPSS).
FIGURE 8.9: Summary statistics for the diameter of Eagle Boy's and Domino's large pizzas, from jamovi
FIGURE 8.10: Summary statistics for the diameter of Eagle Boy's and Domino's large pizzas, from SPSS
Explain whether the study is observational or experimental (true or quasi).
Identify the type of research question is being answered: descriptive, relational, repreated-measures or correlational? Explain.
Two students are arguing about this study. One claims that the study compares two independent samples, because the pizzas have come from two different companies completely. The other student argues that the study has paired samples, because each store has the same types of pizzas in the sample (e.g. both have supreme, Hawaiian and meat-lovers pizzas).
With whom do you agree? Why?
Write down the CI to estimate the difference in population means.
Write a statement communicating the confidence interval.
What does the right panel of Fig. 8.11 communicate?
What condition must hold for the CI to be statistically valid?
Is it reasonable to assume these conditions are satisfied? (You may need to refer Fig. 8.11.)
Eagle Boy's claimed that their pizzas are 'larger' than Domino's pizzas. Do you agree or disagree?
Why? What other information would be helpful for answering this question?
FIGURE 8.11: Boxplot (left panel) and error-bar chart (right panel) for the pizza size data
8.6.3 Optional: Odds and odds ratio
The use of genetically modified (GM) foods is controversial. An Australian study (Luo et al. 2004) decided to study:
...whether income level and attitude to genetic engineering of food are dependent.
To answer this relational RQ, the researcher asked 894 Australians about their income (low or high), and their attitude to GM foods (for or against).
- The data collected are given in Table 8.3. Compute the odds that, among high-income earners, someone is in favour of GM foods.
- Compute the odds that, among low-income earners, someone is in favour of GM foods.
Interpret what this means. - The odds of a high-income earner being in favour of GM foods is how many times more than a low-income earner being in favour of GM food? This value is called the odds ratio.
- For these data, the output is shown in Fig. 8.12 (from jamovi). Write down the confidence interval for the odds ratio, and interpret what this means.
- A politician stated that 'any attempt to suggest that the acceptance of GM foods is related to income are clearly bogus'. Do you agree or disagree?
| High income | Low income | |
|---|---|---|
| For GM foods | 263 | 258 |
| Against GM foods | 151 | 222 |
FIGURE 8.12: jamovi output for the GM foods data