Here are summary statistics for randomly selected weights of newborn girls: n equals = 186 186, x overbar x equals = 27.7 27.7 hg, s equals = 6.2 6.2 hg. Construct a confidence interval estimate of the mean. Use a 95 95% confidence level. Are these results very different from the confidence interval 26.2 26.2 hg less than < mu μ less than < 28.2 28.2 hg with only 16 16 sample values, x overbar
Solution :
Given that,
Point estimate = sample mean = = 27.7
sample standard deviation = s = 6.2
sample size = n = 186
Degrees of freedom = df = n - 1 = 186 -1 = 185
At 95% confidence level
= 1-0.95% =1-0.95 =0.05
/2
=0.05/ 2= 0.025
t/2,df
= t0.025,185 = 1.97
t /2,df = 1.97
Margin of error = E = t/2,df * (s /n)
=1.97 * (6.2 / 186)
Margin of error = E = 0.897
The 95% confidence interval estimate of the population mean is,
- E < < + E
27.7 - 0.897 < < 27.7 + 0.897
26.303 < < 28.097
(26.303,28.097)
Here are summary statistics for randomly selected weights of newborn girls: n equals = 186 186,...
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