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Chapter 4: Q. 93 (page 280)

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 50students or an SRS of 100students? Explain your answer.

Short Answer

Expert verified

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

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

Step by step solution

01

Part (a) Step 1: Given Information 

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

02

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.

03

Part (b) Step 1: Given Information

We are given two random samples of students.

50students random samples

100students random samples

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

04

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.

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