Question

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

Answer #1

a)

i) 90% confidence interval estimate for population mean is,

The 90% confidence interval is, **(24.80,
25.80)**

ii) 95% confidence interval estimate for population mean is,

The 95% confidence interval is, **(24.71,
25.89)**

iii) 99% confidence interval estimate for population mean is,

The 99% confidence interval is, **(24.52,
26.08)**

b)

i) Margin of error ( E ) for 90% confidence interval is,
**0.4987**

ii) Margin of error ( E ) for 95% confidence interval is,
**0.5942**

iii) Margin of error ( E ) for 99% confidence interval is,
**0.7821**

We have the survey data on the body mass index (BMI) of 659
young women. The mean BMI in the sample was x¯=25.5. We treated
these data as an SRS from a Normally distributed population with
standard deviation σ=7.8 .
Give confidence intervals for the mean BMI and the margins of
error for 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?
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An NHANES report gives data for 644 women aged 20–29 years. The
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women in this age group. We treated these data as an SRS from a
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(
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How large a sample would be needed to estimate the mean BMI µ in
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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...

(18.12) Example 16.1 assumed that the body mass index (BMI) of
all American young women follows a Normal distribution with
standard deviation ? = 7.5.
How large a sample would be needed to estimate the mean BMI ? in
this population to within ±1 with 95% confidence?
Give your answer as a whole number.
Fill in the blank:

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....

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
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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 647 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 = 7.39. What is the 95%
t confidence interval for the mean BMI of all young women?...

The body mass index (BMI) for a sample of men and a sample of
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Men
23.8
22.3
32.9
27.4
27.5
31.7
25.9
23.3
22.1
25.7
Women
17.5
21.5
22.6
31.8
17.9
20.6
17.2
38.3
19.5
24.6
Construct a 99% confidence interval estimate of the standard
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_ < σ men < _
Construct a 99% confidence interval estimate of...

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