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Answer :
(a) The 95% confidence interval estimate of the population proportion of adults who had bought something online can be calculated using the formula:
[phat - 1.96 * sqrt((phat * (1 - phat)) / n), phat + 1.96 * sqrt((phat * (1 - phat)) / n)],
where phat is the sample proportion and n is the sample size.
Given that 1,882 out of 2,448 adults had bought something online, the sample proportion is phat = 1,882/2,448 ≈ 0.7686.
Using the formula, the confidence interval estimate is approximately [0.7516, 0.7856].
(b) To calculate the confidence interval, we used a critical value of 1.96 for a 95% confidence level. This value is based on the standard normal distribution and represents the number of standard deviations corresponding to the desired confidence level.
(c) We can be 95% confident that the true population proportion of adults who have bought something online falls within the interval [0.7516, 0.7856]. This means that if we were to repeat the survey many times, we would expect the proportion of online shoppers in the population to fall within this range in approximately 95% of the cases.
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