The correct answer is D) Different random samples will include different students and produce different estimates, which means there's no guarantee the sample result will match the true population proportion exactly. This is due to variability inherent in random sampling.
The question addresses whether the sample result will be exactly the same as the true population proportion when surveying how many students at a school use Titter.
The correct answer is D) Different random samples will include different students and produce different estimates, so there is no guarantee that your sample result will equal the population proportion.
This is because while a simple random sample is designed to be representative of the population, it is only an estimate of the true proportion.
In practice, each sample may contain different individuals and hence may yield different proportions.
When you collect categorical data like Yes/No responses, you are dealing with a proportion problem.
According to the central limit theorem for proportions, the distribution of sample proportions will follow a normal distribution with a mean equal to the population proportion (p) and a standard deviation determined by the formula for standard error of the proportion which is √pq/n (where q = 1 - p).