Answer :
All three conditions for inference are met, the doctor can proceed with constructing a confidence interval for the true proportion of adults who eat an apple a day.
What is 98% confidence interval?
An interval with a 98% confidence level suggests that if the doctor repeated the sampling procedure numerous times and created a confidence level with each sample, around 98% of those intervals would contain the actual percentage of adults who eat an apple every day. With a sample of 200 persons, the doctor can be 98% confident that the actual proportion of adults who eat an apple every day falls between 0.046 and 0.194. While the true proportion is a fixed figure, it is crucial to highlight that this interpretation does not imply that there is a 98% likelihood that it is within this range (although unknown).
The reference conditions for the given situation are:
Random condition: This requirement is satisfied because the doctor chose a random sample of 200 adults.
10% condition: As the sample size is substantially less than 10% of the population (200), this requirement is also satisfied.
High numbers requirement: The doctor must determine whether both the success rate (the proportion of adults who eat an apple every day) and the failure rate (the proportion of adults who don't) are at least 10. In this instance, there were 24 successes and 200 failures, which equals 176. As both of these sums are more than 10, the requirement for big counts is likewise satisfied.
Since all three conditions for inference are met, the doctor can proceed with constructing a confidence interval for the true proportion of adults who eat an apple a day.
Learn more about confidence interval here:
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