If sample size is bigger in random sampling, which of the following is TRUE –
**Core Concept**
Random sampling is a statistical technique used to select a representative subset of individuals from a larger population. A key aspect of random sampling is the sample size, which affects the reliability and accuracy of the results. Increasing the sample size can provide a more precise estimate of the population parameters.
**Why the Correct Answer is Right**
When the sample size is bigger in random sampling, it leads to a more precise estimate of the population mean and standard deviation. This is because a larger sample size provides more data points, which in turn reduces the standard error of the mean (SEM). The SEM is a measure of the variability in the sample mean, and a smaller SEM indicates that the sample mean is a more reliable estimate of the population mean. As the sample size increases, the SEM decreases, making the estimate of the population mean more accurate.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because increasing the sample size in random sampling does not necessarily lead to a more accurate estimate of the population proportion. While a larger sample size can provide more precise estimates of proportions, it's not the primary benefit of increasing the sample size in random sampling.
**Option B:** This option is incorrect because increasing the sample size in random sampling does not directly affect the sample variance. The sample variance is a measure of the spread of the data points in the sample, and it's not directly affected by the sample size.
**Option C:** This option is incorrect because increasing the sample size in random sampling does not necessarily lead to a more accurate estimate of the population standard deviation. While a larger sample size can provide more precise estimates of standard deviations, it's not the primary benefit of increasing the sample size in random sampling.
**Clinical Pearl / High-Yield Fact**
A key takeaway from random sampling is that increasing the sample size can provide a more precise estimate of the population parameters, but it's essential to consider the sampling method, sample size, and population characteristics when designing a study.
**Correct Answer: B. Increasing the sample size in random sampling leads to a more precise estimate of the population parameters, which is reflected in a decrease in the standard error of the mean (SEM).**