Here are summary statistics for randomly selected weights of newborn girls: n=238, x=26.6 hg, s=6.5 hg. Construct a confidence interval estimate of the mean. Use a 99% confidence level. Are these results very different from the confidence interval 25.1 hg< mu <28.3 hg with only 17 sample values, x = 26.7 hg, and s=2.2 hg?
Solution :
Given that,
Point estimate = sample mean = = 26.6 hg
sample standard deviation = s = 6.5 hg
sample size = n = 238
Degrees of freedom = df = n - 1 = 238 - 1 = 237
At 99% confidence level
= 1 - 99%
=1 - 0.99 =0.01
/2
= 0.005
t/2,df
= t0.005, 237 = 2.597
Margin of error = E = t/2,df * (s /n)
= 2.597 * (6.5 / 238)
Margin of error = E = 1.1
The 99% confidence interval estimate of the population mean is,
- E < < + E
26.6 - 1.1 < < 26.6 + 1.1
(25.5 < < 27.7)
Here are summary statistics for randomly selected weights of newborn girls: n=238, x=26.6 hg, s=6.5 hg....
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