On average, a sample of n=100 scores will provide a better estimate of the population mean than would be obtained from a sample of n=50 scores. (True or False)
True, assuming both are random.
False.
Well, it's like picking candy from a bowl. The more candy you have, the more likely you're getting an accurate representation of the flavors. In this case, a larger sample size will provide a better estimate of the population mean. So, n=100 is more likely to give you a sweeter estimate than n=50. Keep sampling those candies, I mean, scores!
True.
A larger sample size generally provides a better estimate of the population mean. With a sample size of 100, there is a higher chance of capturing the variability and characteristics of the population compared to a sample size of 50. A larger sample size reduces the impact of random sampling error and leads to more precise estimates of the population mean.
True.
To understand why this statement is true, we need to consider the concept of sampling error. Sampling error refers to the discrepancy between a sample statistic (such as the sample mean) and the corresponding population parameter (such as the population mean).
A larger sample size generally leads to a smaller sampling error, which means that the sample mean is likely to be closer to the population mean. This is because larger samples provide more information about the population, reducing the potential impact of random variability.
When comparing two sample sizes, n=100 and n=50, the sample of n=100 scores is larger, which means it has a higher chance of providing a more accurate estimate of the population mean compared to the sample of n=50 scores.
However, it's important to note that the relative improvement in the estimate decreases as the sample size increases. In other words, going from n=10 to n=20 might yield a larger improvement in the estimate than going from n=100 to n=200. Nonetheless, in general, larger sample sizes tend to provide better estimates of the population mean.