When does the t-distribution approach the standard normal distribution? A) When

Question

When does the t-distribution approach the standard normal distribution?

A) When the sample size increases, because the standard deviation of the distribution of sample means better estimates the population standard deviation for larger sample sizes

B) When the sample size decreases, because the standard deviation of the sample data better estimates the population standard deviation for smaller sample sizes

C) When the standard deviation of the sample data becomes larger, as larger sample standard deviations better estimate population standard deviations

D) When the sample size increases, because the standard deviation of the sample data better estimates the population standard deviation for larger sample sizes

E) When the sample size decreases, because the standard deviation of the distribution of sample means better estimates the population standard deviation for smaller sample sizes

Explanation / Answer

Actually, t - distribution comes under Exact distribution its means that, the size of the sample is small i.e less than 30 observations. this distribution becomes standard normal distribution if and only if the degree of freedom increase. degree of freedom increase means the size of the sample increases in the random sample. as we know that if sample size increases the estimate of the parameter is more efficient.

"When the sample size increases, because the standard deviation of the sample data better estimates the population standard deviation for larger sample sizes" is correct options

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