What happens to the shape of sampling distribution of sample means as n increases?Regardless of the distribution of the population, as the sample size is increased the shape of the sampling distribution of the sample mean becomes increasingly bell-shaped, centered on the population mean. Show What happens to the sampling distribution as n gets large?As the sample size (n) increases, the standard deviation of the sampling distribution becomes smaller because the square root of the sample size is in the denominator. In other words, the sampling distribution clusters more tightly around the mean as sample size increases.
How does the shape of at distribution change as the sample size increases explain?As explained above, the shape of the t-distribution is affected by sample size. As the sample size grows, the t-distribution gets closer and closer to a normal distribution. Theoretically, the t-distribution only becomes perfectly normal when the sample size reaches the population size.
What is the shape of the sampling distribution of the sample mean?The Shape of the Sample Mean Distribution is Normal!
The sample mean distribution is a heap shaped, as in the shape of the normal distribution, and centered on the population mean. If the sample size is 30 or more, then the sample means are NORMALLY distributed even when the underlying data is NOT normally distributed!
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