Question

The pH of 20 randomly selected lakes is measured. Their average pH is 5.7.

Part A. Historically the standard deviation in the pH values is
0.9. Use this standard deviation for the following questions.

Part Ai. Build a 95% confidence interval for the population mean
lake pH.

Part Aii. Build a 90% confidence interval for the population mean
lake pH.

Part Aiii. Build an 80% confidence interval for the population mean
lake pH.

Part Aiv. Compare the intervals you created in Ai, Aii and Aiii.
What effect does changing the level of confidence have on the
interval?

Please solve part B

Part B. For the 20 measured lakes the standard deviation in the
pH values is 0.9. Use this standard deviation for the following
questions.

Part Bi. Build a 95% confidence interval for the population mean
lake pH.

Part Bii. Compare the confidence intervals in Bi and Ai. What
effect does not knowing the value of ? have on the interval?

Part Biii. Test whether the population mean pH differs from 6.

Answer #1

The caloric consumption of 38 adults was measured and found to
average 2,136. Assume the population standard deviation is 270
calories per day. Construct confidence intervals to estimate the
mean number of calories consumed per day for the population with
the confidence levels shown below.
a.92%
b.95%
c.99%
a. The 92% confidence interval has a lower limit of and an upper
limit of .

1.) As part of an environmental studies class project, students
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trees near Brainard Lake, Colorado. The sample mean circumference
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B. In a representative sample
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A researcher measured the body temperatures of a randomly
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collected are presented in the table below. Complete parts? (a)
through? (d) below.
Summary
Count
Mean
Median
MidRange
StdDev
Range
IntQRange
tempeture
43
98.457
98.000
98.600
0.8847
2.800
1.050 ?
a) Would a 90?% confidence interval be wider or narrower than
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The random sample shown below was selected from a
normal distribution.
5,5,8,9,4,5
A. Construct a 95% confidence interval for the population
mean.
B. Assume that sample mean x and sample standard deviation s
remain exactly the same as those you just calculated but that are
based on a sample of n=25 observations. repeat part a. what is the
effect of increasing the sample size on the width of the confidence
intervals?

The caloric consumption of 44 adults was measured and found to
average 2,117. Assume the population standard deviation is 251
calories per day. Construct confidence intervals to estimate the
mean number of calories consumed per day for the population with
the confidence levels shown below.
a.
93 %
b.
96 %
c.
98 %
a. The 93 % confidence interval has a lower limit of and an
upper limit of

The trout in a lake have historically had an average weight of
11.2 pounds. It is suspected that pollution from a nearby factory
has affected the weight of trout in recent years.
Suppose you take a random sample of 50 trout from the lake, and
you find that the sample mean of their weight is 10.2 pounds, with
a sample standard deviation of 2.1 pounds.
(a) The standard error of the (sample) mean is
___________________________
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•Let’s say Joe measures the average cross section area of pvc
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a.) Calculate the 90% and 95% confidence
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b.) What are the Margin of errors for 90% confidence and
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As part of a water quality survey, you test the water hardness
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Construct a confidence interval for the population variance sigma
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level of confidence. Assume that the population has a normal
distribution.
nequals=23
sequals=16 grains per gallon

Suppose you have selected a random sample of ?=14 measurements
from a normal distribution. Compare the standard normal ? values
with the corresponding ? values if you were forming the following
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(a) 90% confidence interval
z=
t=
(b) 95% confidence interval
z=
t=
(c) 98% confidence interval
?=
t=
2) A confidence interval for a population mean has length
20.
a) Determine the margin of error.
b) If the sample mean is 58.6, obtain the confidence
interval.
Confidence interval: ( ,...

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