Question

2. An NHANES report gives data for 654 women aged 20 to 29 years. The mean BMI for these 654 women was x = 26.8. On the basis of this sample, we are going to estimate the mean BMI μ in the population of all 20.6 million women in this age group. We will assume that the NHANES sample is a SRS from a normal distribution with known standard deviation σ = 7.5

a) Construct 3 confidence intervals for the mean BMI m in this population using 90%, 95%, and 99% confidence.

b) What are the margin of errors for 90%, 95% and 99% confidence.

c) How does increase in confidence level change the margin of error when the sample size and population standard deviation remain the same?

d) Suppose we have a SRS of just 100 young women. What would the margin of error for 95% confidence?

e) Find the margin of error for 95% confidence based on SRSs of 400 young women.

f) Find the margin of error for 95% confidence based on SRSs of 1600 young women.

g) Compare the three margin of errors. How does the increase in sample size change the margin of error when the confidence level and population standard deviation remain the same.

Answer #1

An NHANES report gives data for 644 women aged 20–29 years. The
BMI of these 644 women was ?¯= 27 . On the basis of this sample, we
want to estimate the BMI ? in the population of all 20.6 million
women in this age group. We treated these data as an SRS from a
Normally distributed population with standard deviation ?=7.8 .
(
a) Suppose we had an SRS of just 90 young women. What would be
the margin...

An NHANES report gives data for 647 women aged 20–29 years. The
BMI of these 647 women was ?¯= 25.8 . On the basis of this sample,
we want to estimate the BMI ? in the population of all 20.6 million
women in this age group. We treated these data as an SRS from a
Normally distributed population with standard deviation ?=7.1 .
(a) Give three confidence intervals for the mean BMI ? in this
population, using 90%,95%,and 99% confidence....

Example 14.1 (page 360) described NHANES survey data on the body
mass index (BMI) of 654 young women. The mean BMI in the sample was
x¯¯¯x¯ = 26.8. We treated these data as an SRS from a Normally
distributed population with standard deviation σσ = 7.5.
(a) Give three confidence intervals for the mean BMI μμ in this
population, using 90%, 95%, and 99% confidence.
(b) What are the margins of error for 90%, 95%, and 99% confidence?
How does...

We have the survey data on the body mass index (BMI) of 662
young women. The mean BMI in the sample wasx¯¯¯=25.3x¯=25.3. We
treated these data as an SRS from a Normally distributed population
with standard deviationσ=σ=7.8 .
Give confidence intervals for the true population mean BMI and
the margins of error for 90%, 95%, and 99% confidence.
Conf. Level Interval (±±0.01) margins of error (±±0.0001)
90% to
95% to
99% to

490/654 Venezuelan women from the armed forces said they were
not interested in American Football. A 95% confidence interval for
the proportion with no interest in American Football is 0.70 to
0.80.
A) What would margin of error be for the CI of this
proportion?
Wouldn't this just be 10%?
B) We then sampled 1568 more Venezuelan woman. They were also
asked if they had interest in American Football. If we constructed
another CI based on this sample, how would...

Find the margin of error for a 95% confidence interval for
estimating the population mean when the sample standard deviation
equals 90 with a sample size of (i) 484 and (ii) 1600
(i) Find the margin of error for a 95% confidence interval for
estimating the population mean when the sample standard deviation
equals 90 with a sample size of 484
(ii).
(ii) Find the margin of error for a 95% confidence interval
for estimating the population mean when the...

2.
Based on a sample data of 64 children mean age of children in the
summer camp A is 12,4 years with Standard deviation 3 years.
Estimate the average age of children in whole population.
Population size is 8100
a) Find the point estimation for average age
b) With 95% confidence, what is the margin of error? With 90%
confidence, what is the margin of error?
c) What is the 95% confidence interval estimate of the population
mean (mean children...

A group of researchers developed a 95% z confidence interval for
the mean body mass index (BMI) of women aged 20 to 29 years, based
on a national random sample of 633 such women. They assumed that
the population standard deviation was known to be σ = 7.5. In fact,
the sample data had mean BMI x = 26.9 and standard deviation s =
7.55. What is the 95% t confidence interval for the mean BMI of all
young women?...

The distribution of heights of women aged 20 to 29 is
approximately Normal with mean μ = 67.0 inches and
standard deviation σ = 2.9 inches. (Enter your answers to
one decimal place.)
The height of the middle 95% of young women falls between a low
of ______inches and a high of_____ inches.

Assume that you want to construct a 95% confidence interval
estimate of a population mean. Find an estimate of the sample size
needed to obtain the specified margin of error for the 95%
confidence interval. The sample standard deviation is given
below.
Margin of errors=$6,
standard deviation=$22
The required sample size is __

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