states that the sampling distribution of x is approximately normal when the sample is large.
Question
states that the sampling distribution of x is approximately normal when the sample is large.
Solution
This statement is referring to the Central Limit Theorem. The Central Limit Theorem 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). If the population is normal, then the theorem holds true even for samples smaller than 30. In other words, if the sample size is large enough, the sampling distribution of the mean will be approximately normal.
Similar Questions
The sampling distribution of sample mean for a large population is approximately normal if the sample size is
The sampling distribution of sample mean for a large population is approximately normal if the sample size isans.
The sampling distribution of sample mean for a large population is approximately normal if the sample size is ans. 5 10 100 2
When the population is not normally distributed, the sampling distribution of the mean approximates which of the following? A normal distribution A normal distribution given a large enough sample A slight positive skew A distribution that is not normal
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.
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