Question 1182728: Here are summary statistics for randomly selected weights of newborn girls: n = 175, x̄ = 29.5 hg, s = 6.8 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 27.6 hg < μ < 31.0 hg with only 16 sample values, x̄ = 29.3 hg, and s = 2.6 hg?
Are the results between the two confidence intervals very different?
A. No, because the confidence interval limits are similar.
B. Yes, because the confidence interval limits are not similar.
C. No, because each confidence interval contains the mean of the other confidence interval.
D. Yes, because one confidence interval does not contain the mean of the other confidence interval.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 98% half-interval is t(df=174)*s/sqrt(n). Could use z in this instance with large n and likely normal distribution or close enough.
=2.348*6.8/sqrt(175)
=1.21
the interval is (28.29, 30.71) units hg
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with 16 the calculations are 2.348*2.6/4=1.53
interval is (27.77, 30.83)
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These overlap, but more importantly they overlap a great deal, suggesting that there two intervals are similar despite differing sample size.
A two sample t-test shows no significant difference suggesting strongly that the two samples are indeed coming from the same population.
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