True or false: The standard deviation of the sampling distribution of x¯ gets smaller as the sample size increases.
TrueThe formula for the standard deviation of the sampling distribution of x¯ is σ/n−√. Since the sample size is in the denominator, the standard deviation of the sampling distribution gets smaller as the sample size increases.
True.
As the sample size increases, the standard deviation of the sampling distribution of x¯ decreases, assuming that the population standard deviation is known. This can be shown mathematically using the formula:
Standard deviation of sampling distribution of x¯ = σ/√n
where σ is the population standard deviation and n is the sample size.
As n gets larger, the denominator of this formula increases, resulting in a smaller value for the standard deviation of the sampling distribution of x¯. This is beneficial because it indicates that larger sample sizes have less sampling variability and are more likely to produce a statistic (such as x¯) that is close to the true population parameter.
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