Final answer:
The true statement among the given options is (a) The sample mean is an unbiased estimate of the population mean. The other statements are false because the z-critical and t-critical values are related to hypothesis testing, not estimation of the population parameters, and the sample standard deviation is a biased estimator for the population standard deviation.
Step-by-step explanation:
The question is assessing knowledge of statistical concepts, particularly estimation and hypothesis testing. Let's examine each statement individually:
a) The sample mean is an unbiased estimate of the population mean. This statement is true. The mean of a sampling distribution of the means will equal the population mean, according to the Central Limit Theorem.
b) The z-critical value is an estimate of the population mean. This statement is false. The z-critical value is used in hypothesis testing to determine the cutoff points for the rejection regions in a standard normal distribution, not as an estimate of the population mean.
c) The t-critical value is an estimate of the population standard deviation. This statement is false. The t-critical value is used in hypothesis testing, specifically with the t-distribution when the population standard deviation is unknown and the sample standard deviation is used as an estimate.
d) The sample standard deviation is an unbiased estimate of the population standard deviation. This statement is generally false because the sample standard deviation is a biased estimator of the population standard deviation, especially for small sample sizes. However, it can be made unbiased by using correction factors.