Here are summary statistics fro randomly selected weights of

kuhse4461a

kuhse4461a

Answered question

2021-12-13

Here are summary statistics fro randomly selected weights of newborn girs:
n=240, x=26.1hg, s=6.3hg
Construct a confidence interval estimate of the mean. Use a 99% confidence level. Are these results very different from the confidence interval
25.1hg<μ<28.1hg
with only 13 sample values,
x=26.6hg and s=1.8hg?
What is the confidence interval for the population mean μ?
Are the results between the two confidence intervals very different?
a) No, because each confidence interval contains the mean of the other confidence interval.
b) No, because the confidence interval limits are similar.
c) Yes, because the confidence interval limits are not similar.
d) Yes, because one confidence interval does not contain the mean of the other confidence interval.

Answer & Explanation

movingsupplyw1

movingsupplyw1

Beginner2021-12-14Added 30 answers

Step 1
The confidence interval is used to infer about the population parameter. The confidence interval provides the range of plausible values of the population parameter.
If the sample size is sufficiently large, the confidence interval can be estimated by the standard normal distribution and the confidence interval is given by
x±z×(sn)
When the sample size is small the confidence interval is computed using the students
porschomcl

porschomcl

Beginner2021-12-15Added 28 answers

Step 1
Given:
n=240
x=26.1 hg
s=6.3 hg
σ=0.01
Step 2
99%Cl:
(xtn1, α2×sn<μ<x+tn1, α2×sn)
(26.1t239, 0.005×6.3240<μ<26.1+t239, 0.005×6.3240)
(26.12.5965562×6.3240<μ<26.1+2.5965562×6.3240)
(25.0 hg<μ<27.2 hg)
This interval is n  compared to
25.1 hg<μ<28.1 hg
with,
n=13, s=1.8 hg, x=26.6 hg

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