Question

- Calculate the 99%, 95%, and 90% confidence intervals for the
following information. Identify how these confidence intervals are
similar and how they are different. Explain why.
**(70 points)**

µ = 89 σ = 9 n = 121

- The 99% Confidence Interval:

- The 95% Confidence Interval:

- The 90% Confidence Interval:

- Similarities:

- Differences:

- Why?

Answer #1

1) The 90% confidence interval is ,

Margin of error=E=1.3418

Width of the confidence interval=90.3418-87.6582=2.6836

2) The 95% confidence interval is ,

Margin of error=E=1.6037

Width of the confidence interval=90.6037-87.3963=3.2074

3) The 99% confidence interval is ,

Margin of error=E=2.1110

Width of the confidence interval=91.1110-86.8890=4.2220

4) The standard error is similar. S.E.=

5) Now , the confidence intervals are different because as the confidence level increases , then the margin of error increases.

Also , as the confidence level increases , then the width of the confidence interval increased.

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. 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...

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. 13.1 11.6 11.9 12.0
12.5 11.4 12.0 11.7 11.8 13.1 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...

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. 12.0 11.6 11.9 12.9
12.5 11.4 12.0 11.7 11.8 12.0 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...

1. Develop 90 %, 95 %, and 99% confidence intervals for
population mean (µ) when sample mean is 10 with the sample size of
100. Population standard deviation is known to be 5.
2. Suppose that sample size changes to 144 and 225. Develop
three confidence intervals again. What happens to the margin of
error when sample size increases?
3. A simple random sample of 400 individuals provides 100 yes
responses. Compute the 90%, 95%, and 99% confidence interval for...

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_________.

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...

Use the following information to construct the confidence
intervals specified to estimate μ.
a. 95% confidence for x¯ = 20, σ = 2.5,
and n = 60
b. 98% confidence for x¯ = 124.6, σ =
19.89, and n = 78
c. 90% confidence for x¯ = 2.419, σ =
0.868, and n = 34
d. 80% confidence for x¯ = 54.7, σ = 8.1,
N = 500, and n = 48

Below are three confidence intervals for a sample mean of 16
minutes...
90%, 95%, 99%. Select the 99% confidence interval.
(a) 12 to 20 minutes
(b) 13 to 19 minutes
(c) 14 to 18 minutes

A researcher computed 90%, 95%, 98% and 99% confidence intervals
for a population mean. However, he forgot to record which interval
was which, and he cannot find the sample data to allow him to
recreate the intervals from scratch. He now needs only the 99%
confidence interval. Which one is it?
a-(37.9, 42.1)
b-(38.4, 41.6)
c-(38.1, 41.9)
d-(38.7, 41.3)

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