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What proportion of students at your school use Twit? 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.

1 Answer

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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. Hence the correct option is d.

When you conduct a simple random sample, you are selecting a subset of the population in a way that each individual has an equal chance of being chosen. However, due to the inherent variability in random sampling, different random samples will likely include different students.

This variability is known as sampling error. The larger the sample size, the smaller the sampling error tends to be, but it can never guarantee an exact match between the sample result and the true population proportion. Therefore, option D acknowledges the inherent variability in sampling and the fact that different random samples may yield different estimates. Hence the correct option is d.

User Matthias Oertel
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