Question

What proportion of students at your school use Twity? To find out, you survey a simple random sample of students from the school roster.

Will your sample result be exactly the same as the true population proportion? Why or why not?

A)Yes, if the sample size is large enough.
B)Yes, if a random sample is selected the sample result will be exactly the same as the true population proportion.
C)No, the sample result will be less than the population proportion.
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.
E)No, the sample result will be greater than the population proportion.

Answer 1

Your sample result from a simple random sample will not be exactly the same as the true population proportion due to sampling error; random samples provide estimates with a level of confidence, not exact figures. Therefore correct option is D

Step-by-step explanation:

When assessing what proportion of students at a school use Twity by surveying a simple random sample of students, your sample result will not be exactly the same as the true population proportion. The correct option is therefore 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 every random sample may vary slightly due to chance and may not perfectly represent the population proportion.

Sampling error is the discrepancy between the sample estimate and the true population parameter, which is always present unless a census of the entire population is conducted. A random sample provides an estimate of the population proportion with some degree of uncertainty described by a margin of error and confidence level, not an exact match.