Question

Here are summary statistics for randomly selected weights of newborn​ girls: nequals 229​, x overbar equals31.3 ​hg, sequels 7.1 hg. Construct a confidence interval estimate of the mean. Use a 90 ​% confidence level. Are these results very different from the confidence interval 30.3 hg less than mules than32.5 hg with only 20 sample​ values, x overbar equals31.4 ​hg, and sequels 2.8 ​hg? What is the confidence interval for the population mean mu ​? Are the results between the two confidence intervals very​ different?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 31.3 hg

sample standard deviation = s = 7.1 hg

sample size = n = 229

Degrees of freedom = df = n - 1 = 229 - 1 = 228

At 90% confidence level

= 1 - 90%

=1 - 0.90 = 0.10

/2 = 0.05

t/2,df = t0.05,228 = 1.652

Margin of error = E = t/2,df * (s /n)

= 1.652 * ( 7.1 / 229)

Margin of error = E = 0.8

The 90% confidence interval estimate of the population mean is,

- E < < + E

31.3 - 0.8 < < 31.3 + 0.8

30.5 hg < < 32.1 hg

Yes, because the confidence interval limits are not similar