Question

Which of the following is true about confidence intervals?

I. If the sample size increases, the width of the confidence
interval tends to increase.

II. If the sample size increases, we will have a higher level of
confidence that the confidence interval contains the parameter.

A) Both (I) and (II).

B) Only (II).

C) Only (I).

D) Neither (I) nor (II).

Answer #1

Correct option :- D ; Neither (I) or (II)

Reason : Option (I) is incorrect since as the sample size
increases, the width of the confidence interval tends to
decrease.

And option (II) is also incorrect since the level of confidence is
(1-level of significane) i.e.

level of confidence = 1 -

Thus, the level of confidence varies with the changes in
values and therefore is not affected by the sample size whereas
the increase in sample size would lead to an increase in the
accuracy.

Hope this answers your query!

As the sample size increases, which of the following are
true:
I) The sample mean tends to fall closer to the population
mean
II) The sampling distribution of the sample mean xbar
approximates the population distribution
III) The standard deviation decreases.
Is the answer for this both I and III? if not please explain
(wasnt sure about II)

1- Which of the following statements is true?
I. For a certain confidence level, you get a higher margin of
error if you reduce your sample size.
II. For a given sample size, increasing the margin of error will
mean higher confidence.
III. For a fixed margin of error, smaller samples will mean
lower confidence.
I only
II only
III only
II and III only
All of them
----------------------------------
2- Which must be true about a 90% confidence interval based...

Which of the following statements about confidence intervals are
true?
I. A 95% confidence interval will contain the true μ 95% of the
time.
II. If P(|X̅ − μ| > 3) = 0.035. Then a value of μ that is 3
or less units away from X̅ will be included in the 99% confidence
interval.
III. The point estimate X̅ will be included in a 99% confidence
interval.

Which of the following statements about long-term care insurance
is (are) TRUE?
I. It is no longer needed once a person is eligible for
Medicare.
II. Purchasers have a choice of daily benefits and benefit
periods.
I only
II only
Both I and II
Neither I nor II

1.Simulate 100 confidence intervals with a 90% confidence level.
Choose a sample size between 2 and 20. Look at your confidence
intervals. Take note of their width. Now increase the sample size
to something between 30 and 100. Look at your confidence intervals.
Finally, increase your sample size to 1000. Look at your confidence
intervals. How does sample size affect your confidence intervals?
Explain.
2. Simulate 100 confidence intervals with a 90% confidence
level. Choose a sample size between 30...

Which of the following is TRUE?
A.
The confidence interval is narrower if the sample size is
smaller.
B.
The confidence interval is narrower if the level of significance
is smaller.
C.
The confidence interval is wider if the level of confidence
level is larger.
D.
The confidence interval is wider if the sample size is
larger.

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.

Identify whether the corresponding statements are
correct or incorrect
a) As sample size increases, confidence intervals narrow
.
b) As confidence levels increase, the confidence interval
narrows.
c) If 2 variables have high correlation, one could conclude
that a cause and effect relationship is shared between
them.
d) In hypothesis tests, an individual could make the same
conclusion if the decision is based on using confidence intervals
and standardized statistic, but not when using the p value as a
basis....

T or F: As the sample size increases, the length of the
Confidence Interval for the mean decreases.
T or F: As The level of Confidence increases, the length of the
Confidence interval increases.
T or F: To derive the Confidence Interval formula for the mean
where sigma was assumed, we needed the Central Limit Theorem.
T or F: As the estimate for the true mean (i.e. your sample
mean) increases, the length of the associated Confidence Interval
increases as...

Which of the following is correct for confidence interval?
As the sample size decreases, confidence interval gets
narrower.
As the confidence level increases, confidence interval gets
broader.
As the sample size increases, confidence interval gets
broader.
As the confidence level increases, confidence interval gets
narrower.

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