A study takes a SRS from a population of full-term infants. The standard deviation of birth...

A study takes a SRS from a population of full-term infants. The standard deviation of birth weights in this population is 2 pounds. Calculate 95% confidence intervals for μ for samples in which: a) n = 81 and = 7.0 pounds b) n = 9 and = 7.0 pounds c) Which sample provides the most precise estimate of the mean birth weight? d) Interpret the CI you computed in part a).

Solutions

Expert Solution

a) The 95% confidence interval of is given by:

[, ], where, = 7, = 2, n = 81

= [7 - 0.4356, 7 + 0.4356] = [6.5644, 7.4356]. (Ans).

b) The 95% confidence interval of is given by:

[, ], where, = 7, = 2, n = 9

= [7 - 1.3067, 7 + 1.3067] = [5.6933, 8.3067]. (Ans).

c) Since, the 1st confidence interval is smaller in length as compared to 2nd confidence interval, 1st interval is more precise. Also, we know, as sample size increases, the precision of the confidence interval increases. (Ans).

d) The 95% confidence interval in part(a) indicates that we are 95% confident that the population mean will lie within the above interval. (Ans).

orchestra answered 1 year ago

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