Margin of error rules of thumb and confidence intervals for differences
health
A random sample of 1024 Year 12 and 13 students from across New Zealand were asked: 'On a sunny school day, what do you usually do to protect your skin?' (choose ONE main option). 46% chose 'wear a hat', 38% chose 'apply sunscreen' and 16% chose 'nothing' (Figure 1).
Of the sample, 530 were female and 494 were male. Students were also asked whether they applied sunscreen at least once on their most recent sunny school day: 52% of females and 40% of males said they did (Figure 2).
Bar chart of the percentage of 1024 sampled Year 12–13 students choosing each main option: wear a hat, apply sunscreen, nothing.
Bar chart of the percentage of sampled female (n = 530) and male (n = 494) students who said they applied sunscreen at least once on their most recent sunny school day.Facts you may need
(a)
Calculate the margin of error for the survey and construct a 95% CI for the proportion of students who would choose 'wear a hat'.
(b)
A newspaper says: 'More senior students rely on hats than on sunscreen.' Use Figure 1 and a confidence interval to evaluate this claim.
(c)
Use Figure 2 to construct a confidence interval for the difference between the percentage of female and male students who applied sunscreen, and interpret it.
