Question

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 increasing the confidence level change the margin of error
of a confidence interval when the sample size and population
standard deviation remain the same?

(1) 90%: to

95%: to

99%: to

(2) 90%:

Emissions of sulfur dioxide by industry sett off chemical
changes in the atmosphere that result in "acid rain". The acidity
of liquids is measured by pH on a scale of 0 to 14. Distilled water
has pH 7.0, and lower pH values indicate acidity. Normal rain is
somewhat acidic, so acid rain is sometimes defined as rainfall with
a pH below 5.0. Suppose that pH measurements of rainfall on
different days in a Canadian forest follow a Normal distribution
with standard deviation σσ = 0.5. A sample of n days finds that the
mean pH is x¯¯¯x¯ = 4.8. What are the *P-* Values for tests
of sample sizes n = 5, n = 15 and n = 40?

n = 5:

n = 15:

n = 40:

95%:

99%:

Answer #1

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...

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.

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

QUESTION 1:
Emissions of sulfur dioxide by industry set off chemical changes
in the atmosphere that result in "acid rain." The acidity of
liquids is measured by pH on a scale of 0 to 14. Distilled water
has pH 7.0, and lower pH values indicate acidity. Normal rain is
somewhat acidic, so acid rain is sometimes defined as rainfall with
a pH below 5.0. Suppose that pH measurements of rainfall on
different days in a Canadian forest follow a Normal...

Emissions of sulfur dioxide by industry set off chemical changes
in the atmosphere that result in "acid rain." The acidity of
liquids is measured by pH on a scale of 0 to 14. Distilled water
has pH 7.0, and lower pH values indicate acidity. Normal rain is
somewhat acidic, so acid rain is sometimes defined as rainfall with
a pH below 5.0. Suppose that pH measurements of rainfall on
different days in a Canadian forest follow a Normal distribution
with...

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....

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...

The Body Mass Index (BMI) is a value calculated based on the
weight and the height of an individual. In a small European city, a
survey was conducted one year ago to review the BMI of the
citizens. In the sample with 200 citizens, the mean BMI was 23.3
kg/m2 and standard deviation was 1.5 kg/m2. It is reasonable to
assume the BMI distribution is a normal distribution.
(a) Find the point estimate of the population mean BMI one
year...

In a random sample of 50 people, the mean body mass index (BMI)
was 27.7 and the standard deviation (s) was 6.12.
Construct a 90% Confidence interval for the population mean.
Construct a 96% Confidence interval for the population mean.

(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.
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