Question

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 confidence level leads to a wider interval which would still include negative and positive numbers. |

No. Increasing the confidence level leads to a narrower interval so we cannot be sure if the interval would still contain both negative and positive numbers. |

Yes. All 99% confidence intervals for the difference in populations means contain both negative and positive numbers, no matter the situation. |

Not necessarily. We cannot be sure how changing the confidence level will affect the confidence interval. |

Answer #1

The correct answer is A.

**Yes. Keeping all other values the same, increasing the
confidence level leads to a wider interval which would still
include negative and positive
numbers****.**

Because, 95% confidence intervals have the property that they come from a procedure that has a 95% chance of yielding an interval that contains the true value. And if we assume 99% confidence interval, then it yeild 99% true value. Hence 99% confidence interval is widen on both negative and positive sides.

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
include negative and positive numbers.
B.
No. Increasing the confidence level...

A. which confidence interval is wider? The 95%
confidence interval or the 99% confidence interval?
difference for both confidence intervals: 0.109
95% CI for difference: (-0.123, 0.340)
99% CI for difference: (-0.199, 0.416)
B. Given an arbitrary data set, is there a general
relationship between confidence level and the width of the
confidence interval? Explain.
Please make the answers to parts A and B detailed and easy to
read and follow, thank you :)

If you construct a 90% confidence interval for the population
mean instead of a 95% confidence interval and the sample size is
smaller for the 90%, but with everything else being the same, the
confidence interval would: a. remain the same b. become narrower c.
become wider d. cannot tell without further information.

You are constructing a 95% confidence interval for the mean of a
normal population. If you increase your sample size from n to 4n,
the width of the confidence interval a) becomes two times wider b)
becomes two times narrower c) becomes four times narrower d)
becomes four time wider e) cannot determine from this
information
Can somebody explain please? Will upvote :) Thank you

Describe a confidence interval for the difference in means
between two population by stating
1. a pair of populations composed of the same type of individuals
and a quantitative variable on those populations,
2. sizes and degrees of freedom of samples from those
populations,
3. the means of those samples, and
4. the standard deviations of those samples. Then state
5. a confidence level and find
6. find the interval. Finally, perform a test of significance
concerning the difference in...

Find a 95% confidence interval for the difference between the
two population means.

You want to calculate a 95% confidence interval (CI) for the
difference between the means of two variables. The variables are
from populations with normal distributions and those distributions
have the same standard deviation (σ). To make your estimate you
will take the same number of samples from each population,
calculate the mean for each sample, calculate the difference
between those sample means, and then add or subtract the term that
defines the CI. If you want the width of...

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...

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...

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