Evaluating claims in a survey report: CIs, ratio claims, rule-of-thumb limits, causation, non-sampling error
consumer behaviour
A market research company published this summary:
> **Kiwis hooked on delivery** — An online survey of 1250 New Zealand adults (18+) from our research panel was conducted in March. Quotas were set by age, gender and region to match the 2023 Census. 28% of respondents used a food-delivery app at least weekly. Among 18–34 year-olds (n=380) the figure was 47%; among 35–54 year-olds (n=460) it was 27%; among those aged 55+ (n=410) it was 12%. Weekly users reported eating an average of 2.1 servings of vegetables a day, compared with 3.0 for other respondents.
>
> Claims: (1) Nearly half of young New Zealanders use delivery apps weekly. (2) Young New Zealanders are about four times as likely as older New Zealanders to use delivery apps weekly. (3) Using delivery apps weekly leads people to eat fewer vegetables.
Figure 1 is the graph that accompanied the summary.
Useful result: for a sample proportion, the 95% margin of error is 1.96p^(1−p^)/n.
Bar chart from the market research summary showing the percentage of respondents using a food-delivery app at least weekly for ages 18–34 (47%), 35–54 (27%) and 55+ (12%); the vertical axis starts at 10%.Facts you may need
(a)
Evaluate Claim 1 using an appropriate confidence interval.
(b)
Evaluate Claim 2. Include a confidence interval for the difference between the two age groups, and comment on whether the rule-of-thumb method is appropriate here and whether 'about four times as likely' is justified.
(c)
Evaluate Claim 3.
(d)
Discuss TWO possible sources of non-sampling error in this survey and their likely effect on the results.
(e)
Figure 1 accompanied the summary. Critique how Figure 1 presents the age-group results, especially in relation to Claim 2, and describe a better display.
