When the population standard deviation is unknown and the sample size is greater than 30?

In the preceding discussion we have been using s, the population standard deviation, to compute the standard error. However, we don't really know the population standard deviation, since we are working from samples. To get around this, we have been using the sample standard deviation [s] as an estimate. This is not a problem if the sample size is 30 or greater because of the central limit theorem. However, if the sample is small [ t.test[bmi]

The output would look like this: 

One Sample t-test

data:  bmi
t = 228.5395, df = 3231, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
26.66357 27.12504
sample estimates:
mean of x
26.8943

R defaults to computing a 95% confidence interval, but you can specify the confidence interval as follows:

> t.test[bmi,conf.level=.90]

This would compute a 90% confidence interval.

Lozoff and colleagues compared developmental outcomes in children who had been anemic in infancy to those in children who had not been anemic. Some of the data are shown in the table below.

Source: Lozoff et al.: Long-term Developmental Outcome of Infants with Iron Deficiency, NEJM, 1991

Compute the 95% confidence interval for verbal IQ using the t-distribution

Link to the Answer in a Word file

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When the population standard deviation is unknown and the sample size is greater than 30 What table value should be used in computing the confidence interval for mean?

When the sample size is 30 or less and the population standard deviation is unknown we use?

When the population standard deviation is unknown and the sample size is less than 30 t

When n is less than 30 and the population standard deviation is unknown what is the appropriate distribution?