Question

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.

Answer #1

It is true that 95% confidence interval will contain the true mean 95% of the time.

P(|X̅ − μ| > 3) = 0.035

=> P(|X̅ − μ| < 3) = 1 - 0.035

=> P(|X̅ − μ| < 3) = 0.965

=> P(|X̅ − μ| < 3) < 0.99

Then a value of μ that is 3 or less units away from X̅ will be included in the 99% confidence interval.

The point estimate X̅ is the estimate of true mean and will always included in a confidence interval. Thus III is a correct statement.

Thus, all statements I , II and III are true.

1 - Which of the following statements is true regarding a 95%
confidence interval? Assume numerous large samples are taken from
the population.
a. In 95% of all samples, the sample proportion will fall within 2
standard deviations of the mean, which is the true proportion for
the population.
b. In 95% of all samples, the true proportion will fall within 2
standard deviations of the sample proportion.
c. If we add and subtract 2 standard deviations to/from the sample...

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 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).

a. Compute the 95% and 99% confidence intervals on the mean
based on a sample mean of 50 and population standard deviation of
10, for a sample of size 15.
b. What percent of the 95% confidence intervals would you expect
to contain µ? What percent of the 95% confidence intervals would
you expect to contain x̅? What percent of the 95% confidence
intervals would you expect to contain 50?
c. Do you think that the intervals containing µ will...

Construct 90%, 95%, and 99% confidence intervals to estimate μ
from the following data. State the point estimate. Assume the data
come from a normally distributed population. 13.3 11.6 11.9 12.2
12.5 11.4 12.0 11.7 11.8 13.3
(Round the intermediate values to 4 decimal places. Round your
answers to 2 decimal places.)
90% confidence interval: enter the lower limit of the 90%
confidence interval ≤ μ ≤ enter the upper limit
of the 90% confidence interval
95% confidence interval: enter the...

Construct 90%, 95%, and 99% confidence intervals to estimate
μ from the following data. State the point estimate.
Assume the data come from a normally distributed
population.
12.3
11.6
11.9
12.1
12.5
11.4
12.0
11.7
11.8
12.3
(Round the intermediate values to 4 decimal places.
Round your answers to 2 decimal places.)
90% confidence interval:_____________ ≤ μ ≤
_____________
95% confidence interval: ____________ ≤ μ ≤
_____________l
99% confidence interval: ____________ ≤ μ ≤
_____________
The point estimate is_________.

Construct 90%, 95%, and 99% confidence intervals to estimate μ
from the following data. State the point estimate. Assume the data
come from a normally distributed population. 13.7 11.6 11.9 13.0
12.5 11.4 12.0 11.7 11.8 13.7 Appendix A Statistical Tables (Round
the intermediate values to 4 decimal places. Round your answers to
2 decimal places.) 90% confidence interval: enter the lower limit
of the 90% confidence interval ≤ μ ≤ enter the upper limit of the
90% confidence interval...

A 99% confidence interval for a proportion p is (54%, 58%).
Which of the following statements is true:
1. There is a 99% probability that p is between 54% and 58%.
2. If we took indefinitely many independent SRS’s of the same
size and from each computed a 99% confidence interval for p, then
approximately 99% of these intervals would contain p .
3. If we took indefinitely many independent SRS ’ s of the same
size and from each...

Which of the following statements is true with
regards to a confidence interval?
Select one:
a. The true population value is always inside the constructed
interval
b. Most calculations of confidence intervals require a point
estimate and the margin of error
c. Given the same confidence level, building a t-interval is
always narrower than a z-interval
d. A 90% confidence interval means there is a 90% chance the
population value is within the constructed interval
e. You need to know...

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.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 57 seconds ago

asked 5 minutes ago

asked 8 minutes ago

asked 9 minutes ago

asked 19 minutes ago

asked 22 minutes ago

asked 34 minutes ago

asked 34 minutes ago

asked 41 minutes ago

asked 42 minutes ago

asked 42 minutes ago

asked 48 minutes ago