Which statistical test can be used to assess if the sample mean differs significantly from a population mean?

Which statistical test can be used to assess if the sample mean differs significantly from a population mean?

• A. One-sample z score
• B. One-sample z-test
• C. One-sample f-score
• D. One-sample t test

Answer: (B)

The one-sample z-test is a statistical method used to determine whether the sample mean is significantly different from a known population mean when the population variance is known. This test is particularly applicable when dealing with large sample sizes (typically n > 30) due to the Central Limit Theorem, which states that the distribution of sample means will tend to be normally distributed as the sample size increases, regardless of the population's distribution. In a one-sample z-test, the z-score is calculated, which indicates how many standard deviations the sample mean is away from the population mean. This score is then compared against a critical value from the standard normal distribution to determine whether to reject the null hypothesis. If the calculated z-score is greater than the critical value, it suggests that there is a statistically significant difference between the sample mean and the population mean. This test is particularly useful when the sample size is large because the normal distribution can be used more reliably, making interpretation straightforward. It also requires that the population from which the sample is drawn should have a known variance, which is a key condition for using the z-test. In contrast, other options listed involve different statistical methodologies that are not appropriate for this specific question about assessing differences in means. For instance, a

The one-sample z-test is a statistical method used to determine whether the sample mean is significantly different from a known population mean when the population variance is known. This test is particularly applicable when dealing with large sample sizes (typically n > 30) due to the Central Limit Theorem, which states that the distribution of sample means will tend to be normally distributed as the sample size increases, regardless of the population's distribution.

In a one-sample z-test, the z-score is calculated, which indicates how many standard deviations the sample mean is away from the population mean. This score is then compared against a critical value from the standard normal distribution to determine whether to reject the null hypothesis. If the calculated z-score is greater than the critical value, it suggests that there is a statistically significant difference between the sample mean and the population mean.

This test is particularly useful when the sample size is large because the normal distribution can be used more reliably, making interpretation straightforward. It also requires that the population from which the sample is drawn should have a known variance, which is a key condition for using the z-test.

In contrast, other options listed involve different statistical methodologies that are not appropriate for this specific question about assessing differences in means. For instance, a