Question

A 95% confidence interval for the mean trading achievement score for a population of third grade students is (44.2, 54 2). Suppose you compute a 99% confidence interval using the same information. Which of the following statements are correct?

The intervals have the same width

The 99 percent interval is shorter

The 99 percent interval is longer

Answer can't be determined

None of the above

Answer #1

Solution:

Answer is 99% confidence interval is longer.

We know that the confidence interval for the population mean is given by,

Observe that , as the value of increases, the margin of the error increases and the confidence interval becomes the longer. We also know that , as the level of confidence increases , the value of also increases .

So we can say that , as the level of confidence increases , the confidence interval becomes longer.

Answer is 99% confidence interval is longer.

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One can calculate the 95% confidence interval for the mean with
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calculate the 99% confidence interval? Describe how the increase in
the confidence level has changed the width of the confidence
interval. Do the same for the confidence interval set at 80%.
Include an example with actual numerical values for the intervals
in your post to help with...

One can calculate the 95% confidence interval for the mean with
the population standard deviation known. This will give us an upper
and a lower confidence limit. What happens if we decide to
calculate the 99% confidence interval? Describe how the increase in
the confidence level has changed the width of the confidence
interval. Do the same for the confidence interval set at 80%.
Include an example with actual numerical values for the intervals
in your post to help with...

One can calculate the 95% confidence interval for the mean with
the population standard deviation known. This will give us an upper
and a lower confidence limit. What happens if we decide to
calculate the 99% confidence interval? Describe how the increase in
the confidence level has changed the width of the confidence
interval. Do the same for the confidence interval set at 80%.
Include an example with actual numerical values for the intervals
in your post to help with...

Assuming that the population is normally distributed, construct
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samples below. Explain why these two samples produce different
confidence intervals even though they have the same mean and
range.
Sample A: 1 4 4 4 5 5 5 8
Sample B: 1 2 3 4 5 6 7 8
a. Construct a 95% confidence interval for the population mean
for sample A.
b. Construct a 95% confidence interval for...

Which z-score is used in a 95% Confidence interval for a
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B) 1.95
C) 2.66
D) None of the above
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Suppose you calculate a 95% confidence interval for the
difference in population means. The confidence interval contains
both negative and positive values.
Will a 99% confidence interval based on the same data contain
both negative and positive numbers as well? Choose the correct
response from the options provided below.
Yes. Keeping all other values the same, increasing the
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No. Increasing the confidence level leads to...

Suppose you calculate a 95% confidence interval for the
difference in population means. The confidence interval contains
both negative and positive values.
Will a 99% confidence interval based on the same data contain
both negative and positive numbers as well? Choose the correct
response from the options provided below.
A. Yes. Keeping all other values the same, increasing the
confidence level leads to a wider interval which would still
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B.
No. Increasing the confidence level...

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b. What percent of the 95% confidence intervals would you expect
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The following questions ask you to construct and compare
a series of confidence intervals.
A. In a representative sample
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estimate the mean quiz score in the population of all
students. [5 points]
B. In a representative sample
of 100 students, the mean quiz score was 54 points with a standard
deviation of 2 points. Construct a 95%...

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