Question

Here are summary statistics for randomly selected weights of newborn? girls: nequals244?, x overbarequals31.8 ?hg, sequals7.3 hg. Construct a confidence interval estimate of the mean. Use a 99?% confidence level. Are these results very different from the confidence interval 29.3 hgless thanmuless than34.1 hg with only 15 sample? values, x overbarequals31.7 ?hg, and sequals3.1 ?hg? What is the confidence interval for the population mean mu??

Answer 1

Here we have

$n=244,\bar{x}=31.8,s=7.3$

The degree of freedom: df=n-1=243

The critical value for 99% confidence interval is: 2.596

The confidence interval is:

$\bar{x}\pm t_{critical}\frac{s}{\sqrt{n}}=31.8\pm 2.596\cdot \frac{7.3}{\sqrt{244}}=31.8\pm 1.21 =(30.59, 33.01)$

Yes confidence interval with sample size n=15 is larger than above confidence interval.