Question

Discuss how each of the following will affect the width of a confidence interval for estimating a population proportion (in each case assume all other values remain constant):

a) An increase in sample size used to find pˆ

b) A higher confidence level

Answer #1

a.)Confidence Interval:

So, lower and upper limit of the confidence interval will decrease.

b.)as we know

Critical value at 95% confidence=1.96

critical value at 98% confidence=2.33

Critical value at 99% confidence=2.58

so, when confidence level increases due to that the Margin of error part

will increase, as Margin of error increase the **width of
the confidence interval increases.**

Find the minimum sample size needed when estimating population
proportion with 98% confidence level, margin of error to be within
5% and
(a) if pˆ = .768 .
n =
(b) if pˆ is unknown.
n =

Mean
Sample standard deviation
Population standard deviation
Sample size
Confidence level
Confidence interval
100
20
na
25
95 %
100
20
na
25
90 %
100
40
na
25
90 %
100
40
n.a.
16
90 %
100
n.a.
40
16
90 %
How does the confidence level affect the width of the confidence
interval, other things equal?
How does the size of the standard deviation affect the width of
the confidence interval, other things equal?
How does sample size...

How will the width of a confidence interval change (if at all)
in each of the following cases?
A) Sample standard deviation decreases:
a) increase
b) decrease c) stay
the same
B) Sample size decreases:
a) increase
b) decrease
c) stay the same
C) You change from a 95% CI to a 99% CI:
a) increase
b) decrease
c) stay the same

For each of the following situations, state what happens to the
width of the confidence interval. Justify your answers.
A) Population standard deviation increases
B) Sample size decreases (assuming CLT still holds)
C) Confidence level decreases
D) Sample mean increases

The width of a confidence interval
estimate for a population mean when the population standard
deviation is known will
(A) become narrower if the
size of the sample being used is increased and the confidence level
is unchanged.
(B) not change if
only the sample size is increased.
(C) become wider if
the sample size remains the same and the confidence level
decreases.
(D) become narrower if the
size of the sample is decreased and the confidence level is
unchanged....

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...

Which of the following statements is true?
The 95% confidence interval is wider than the 99% confidence
interval.
The ONLY way to reduce the width of a confidence interval is to
reduce the confidence level.
The required sample size for a population mean is ONLY
dependent on population variance.
Given population variance and sampling error, higher confidence
level results in larger sample size.

A researcher is calculating a confidence interval. All other
things being constant, what happens to the width of confidence
interval when the confidence level is increased?
Decreases
Increases
May increase or decrease
Remain the same

The length of a confidence interval changes when either the
confidence level changes or the sample size changes. To illustrate
this, imagine a statistician takes a sample from a population with
a population standard deviation of 2. The sample mean is calculated
to be 10. Construct 3 different confidence intervals:
3a) Assume the sample size is 30 and the confidence level is
95%
3b) Assume the sample size is 30 and the confidence level is
90%
3c) Assume the sample...

True or False:
1. A confidence interval is used for estimating a population
parameter.
2. A confidence interval always captures the sample
statistic.
3. A confidence interval always captures the population
parameter.
4. When constructing a confidence intervals we should always use
Z-critical values.
5. The margin of error determines the center location of the
confidence interval.
6. In general, we would like to have a precise confidence
interval while having a high level of confidence.

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