A sample of size n- 200 has a known population standard deviation of 15.0. The population appears to be skewed. Determine whether a margin of error should be calculated using a critical value of za, a critical value of ta/2, or neither.
A. a critical value of ta/2
B. a critical value of za/2
C. neither
Answer: b. a critical value of za/2, i picked this because the value is greater than 30. Not sure if it’s correct. Please help.
this is correct i just took the test
Well, I'm here to help! Let's break it down.
When determining whether to use a critical value of za or ta/2, we need to consider the sample size (n) and the shape of the population distribution.
First, let's look at the sample size. In general, if the sample size is greater than or equal to 30, it is considered large enough to use a critical value of za for constructing confidence intervals.
However, the shape of the population distribution is also important. Since the population appears to be skewed in this case, it may affect the validity of using a critical value of za.
With all that being said, you are correct! The answer is B. a critical value of za/2. Even though the sample size is greater than 30, the fact that the population appears to be skewed suggests that using a critical value of ta/2 (a t-distribution) would be more appropriate for calculating the margin of error.
Hope that clears things up for you!
To determine whether a margin of error should be calculated using a critical value of za or a critical value of ta/2, we need to consider the sample size and the population standard deviation.
When the sample size (n) is large (usually greater than 30) and the population standard deviation is known, we use a critical value of za. This is because, for large sample sizes, the sampling distribution of the sample mean tends to follow a normal distribution.
In this case, the sample size is not provided, so we cannot deduce the exact value of n. However, since the answer key indicates that the correct choice is a critical value of za/2, we can infer that the sample size is considered large enough to use a critical value of za/2.
Therefore, the correct answer is B. a critical value of za/2.
To determine whether a margin of error should be calculated using a critical value of za, a critical value of ta/2, or neither, we need to consider two factors:
1. Sample Size (n): In general, if the sample size is large (typically n > 30), we can use the z-distribution. If the sample size is small (typically n < 30) and the population standard deviation is unknown, we use the t-distribution.
2. Population Standard Deviation (σ): If the population standard deviation is known, we can use either the z-distribution or the t-distribution.
Based on the information provided in the question, the sample size is not given. However, since you mentioned that it is greater than 30 (n > 30), we can assume that a large sample size is used.
Since the population standard deviation (σ) is known, we can use the z-distribution, and therefore a critical value of za/2 should be used.
Therefore, the correct answer is B. a critical value of za/2.