Final answer:
The true statement regarding the relationship between sampling error and sample size is that the sample size can affect the sampling error. Larger samples lead to smaller errors, making the results more reliable and representative of the entire population.
Step-by-step explanation:
Select the true statement regarding the relationship between sampling error and sample size: a.) The sample size can affect the sampling error. This statement is correct because, as a rule, the larger the sample, the smaller the sampling error. Increasing the sample size causes the error bound to decrease, making the confidence interval narrower. A larger sample size will, therefore, be more representative of the population and minimize the chances of a chance error.
b.) The standard error increases as the sample size increases. This statement is false; in fact, the opposite is true. The standard deviation of the sampling distribution of the means will decrease as the sample size increases.
c.) The smaller a sample size, the more accurate an estimate can be. This statement is false; smaller sample sizes tend to increase the chance that the sample does not represent the population well.
d.) In order to decrease sampling error, you must decrease the sample size. This statement is also false. Decreasing the sample size causes the error bound to increase, making the confidence interval wider, thus increasing the sampling error.
In conclusion, the correct answer is a.) The sample size can affect the sampling error. As the sample size increases, sampling errors tend to decrease, which leads to more reliable and accurate results.