Question

An obstetrician records birth weights of 42 42 newborns she delivers over a two-month period. x⎯⎯⎯=3452 x ¯ = 3452 grams with σ=393.8. σ = 393.8 . She constructs a confidence interval of 3332.9035≤μ≤3571.0965. 3332.9035 ≤ μ ≤ 3571.0965 . What is the confidence level she used to estimate the population mean? Enter your answer as a percentage.

Answer 1

Answer:

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Answer 2

Given :    Mean  $\overline{x}$ =  3452 grams

SD  σ = 393.8  grams

constructs a confidence interval of 3332.9035 ≤μ ≤ 3571.0965.

To Find : confidence level  sed to estimate the population mean

Solution:

Mean  $\overline{x}$ =  3452 grams

SD  σ = 393.8  grams

constructs a confidence interval of 3332.9035 ≤ μ ≤ 3571.0965

Z score = (value - mean)/SD

 Z score for 3332.9035

= (3332.9035 - 3452)/393.8

= -0.3024

≈ 37.3 %

 Z score for 3571.0965

= (3571.0965 - 3452)/393.8

=  0.3024

≈ 62.7 %

confidence level she used to estimate the population mean = 62.7 - 37.3

= 25.4 %

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