Question

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

a. Will your sample result be exactly the same as the true population proportion? Explain your answer.

b. Which would be more likely to produce a sample result closer to the true population value: an SRS of $50$students or an SRS of $100$students? Explain your answer.

Short answer

a.No, our sample result will not be exactly the same as the true population proportion.

b.An SRS of $100$students would be more likely to produce a sample result closer to the true population value than an SRS of $50$students.

Step-by-step solution

Part (a) Step 1: Given Information 

We need to find out whether sample result will be same as true population proportion

Part (a) Step 2: Explanation

No, our sample result will not be exactly the same as the true population proportion because different random samples will produce different statistics, and it is unlikely that this will match that parameter exactly.

Part (b) Step 1: Given Information

We are given two random samples of students.

$50$students random samples

$100$students random samples

We need to explain which sample will give result closer to true population value

Part (b) Step 2: Explanation

An SRS of $100$ students would be more likely to produce a sample result closer to the true population value than an SRS of $50$ students because on increasing the sample size, there is a reduction in the variability.