Question

Nintendo wants to know whether MarioKart is popular amongst students who have access to gaming devices. A manager collected a random sample of 1,000 students with access to gaming devices. He reports that 35% of students in the sample like MarioKart. He correctly reports that the margin of error for a confidence interval estimate for the proportion of students (with access to gaming devices) who like MarioKart is 3 percentage points at a 95% confidence level.

i) State the confidence interval estimate for the proportion of students (with access to gaming devices) who like MarioKart, with confidence of 95%

ii) In the context of this example, explain what is meant by "a confidence of 95%"?

iii) Why are the student observations plausibly independent?

Answer 1

Here we have

Given Sample proportion

and Margin of error (E)=3%

(i) Given and margin of error, . The confidence interval is:

or 32% ,38%

(ii) "A confidence of 95%" means We are 95% confident the population proportion of the student who like MarioKart lies between the interval 32% and 38%.

(iii) Here we can see student observations plausibly independent as proportion of the student who like MarioKart is independent of the liking of each of the student.