What proportion of students at your school use Twitter? To...

Name: Problem 27, Chapter 4: The Practice of Statistics for AP
Uploaded: 2023-03-19T20:33:43-08:00
Duration: 1 min 23 s
Channel: Sheryl Ezze
Description: 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. (b) Which would be more likely to get your sample result closer to the true population value: an SRS of 50 students or an SRS of 100 students? Explain.

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. (b) Which would be more likely to get your sample result closer to the true population value: an SRS of 50 students or an SRS of 100 students? Explain.

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.
(b) Which would be more likely to get your sample result closer to the true population value: an SRS of 50 students or an SRS of 100 students? Explain.

Key Concepts

Simple Random Sampling (SRS)

Simple Random Sampling is a technique where every individual in the population has an equal chance of being selected. This method helps to reduce selection bias and ensures that each sample has the same likelihood of representing the population. The idea is to create a sample that is as representative as possible of the overall population.

Sampling Variability

Sampling variability refers to the natural differences in sample results that occur when different samples are taken from the same population. Because each sample is random, the results such as the proportion of students using Twitter can differ from one sample to another, and they might not match the true population parameter exactly.

Unbiased Estimators

An unbiased estimator is a statistical estimate that, on average, equals the true value of the population parameter. In the context of a simple random sample, the sample proportion is considered an unbiased estimator of the true population proportion, even though individual sample estimates may deviate due to random sampling error.

Sample Size and Precision

Increasing the sample size generally increases the precision of the estimate by reducing the standard error. A larger sample, such as an SRS of 100 students compared to 50 students, is more likely to produce a sample result closer to the true population value because it tends to balance out random fluctuations and provides a more accurate reflection of the population.

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