A researcher takes a simple random sample of 50 recent Science graduates in full-time employment and calculates their mean salary. Which of the following is a true statement about distribution of the sample mean?Select one:a.The Central Limit Theorem tells us it is normal.b.It may not be normal because the sample size is large.c.It may not be normal because we don't know that the population is normal.d.It will not be normal because the sample size is small.
Question
A researcher takes a simple random sample of 50 recent Science graduates in full-time employment and calculates their mean salary. Which of the following is a true statement about distribution of the sample mean?Select one:a.The Central Limit Theorem tells us it is normal.b.It may not be normal because the sample size is large.c.It may not be normal because we don't know that the population is normal.d.It will not be normal because the sample size is small.
Solution
The Central Limit Theorem (CLT) states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30).
Given that the sample size in this case is 50, which is greater than 30, the distribution of the sample mean will be approximately normal according to the Central Limit Theorem.
So, the correct answer is:
a. The Central Limit Theorem tells us it is normal.
Similar Questions
Suppose we take repeated random samples of size 20 from a population with a mean of 60 and a standard deviation of 8. Which of the following statements is true about the sampling distribution of the sample mean (x̄)? Check all that apply. The distribution is normal regardless of the shape of the population distribution, because the sample size is large enough. The distribution will be normal as long as the population distribution is normal. The distribution's mean is the same as the population mean 60. The distribution's standard deviation is larger than the population standard deviation of 8.
Which of the following about the normal distribution is NOT true?
The central limit theorem states that if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean:Group of answer choicesis approximately normal if n ≥ 30.is approximately normal if the underlying population is normal.has the same variance as the population.is approximately normal if n < 30.
The sampling distribution of sample mean for a large population is approximately normal if the sample size is
Which of the following statements about the sampling distribution of the sample mean, x-bar, is true? Check all that apply. The distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough. The distribution is normal regardless of the sample size, as long as the population distribution is normal. The distribution's mean is the same as the population mean. The distribution's standard deviation is smaller than the population standard deviation.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.