Question

True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

If the sample size is at least 30, then you can use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.

Accepted Answer

Step 1: Understand the context of the problem. The statement is about using z-scores to determine probabilities for a sample mean when the sample size is at least 30. This relates to the Central Limit Theorem (CLT), which states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's original distribution. Step 2: Recall the conditions for using z-scores. Z-scores are used when the population standard deviation (σ) is known, and the sampling distribution of the sample mean is approximately normal. For a sample size of at least 30, the CLT ensures that the sampling distribution is approximately normal, even if the population distribution is not normal. Step 3: Evaluate the statement. The statement is true if the population standard deviation (σ) is known. If σ is unknown, you would typically use a t-distribution instead of z-scores, especially for smaller sample sizes. However, for large sample sizes (n ≥ 30), the t-distribution and z-distribution become very similar. Step 4: If the statement is false, rewrite it as a true statement. A true version of the statement would be: 'If the sample size is at least 30 and the population standard deviation is known, then you can use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.' Step 5: Conclude by emphasizing the importance of verifying whether the population standard deviation is known before deciding to use z-scores. If it is unknown, consider using the t-distribution instead.

True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

If the sample size is at least 30, then you can use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Central Limit Theorem

Z-scores

Sampling Distribution

True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.If the sample size is at least 30, then you can use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Central Limit Theorem

Z-scores

Sampling Distribution

True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

If the sample size is at least 30, then you can use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.