The follow data below are teh age of the first word for 21 children, whom we can assume are a random sample of all children.  Age is in months.

Variable    N    Average    Std. Dev.    Min.    Median    Max.
Age            21    14.381    7.9465    7    11    42
 

1. Use these summary statistics and the tables provided to find an 80% confidence interval (NOTE: NOT 85%) for the mean age at which children learn their first word.

Because the population SD is unknown, we use a t-distribution to form the confidence interval.  We want 10% in each of the tails, and there are 20 degrees of
freedom (n-1), so the table gives 1.325 as the correct critical value.  (Note, this assumes the population is normally distributed.  Even if this is not the case, this will hold as a good approximation of the correct confidence interval.)

14.381 +- 1.325*(7.9465/sqrt(21))
14.381 +- 2.29764

Interval is :  (12.0834,  16.6786)

2. (2 pts) If there were more children in the sample, would the confidence interval likely be wider, narrower, or about the same?  Why?
The confidence interval would likely be narrow, because the standard error would be smaller.  Also, as n increases, the degrees of freedom increases, until the t-value used appproaches 1.282 at infinity -- a smaller value which would make the interval smaller.