Question

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.

12.1 | 11.6 | 11.9 | 12.9 | 12.5 | 11.4 | 12.0 |

11.7 | 11.8 | 12.1 |

Answer #1

a)

sample mean, xbar = 12

sample standard deviation, s = 0.4397

sample size, n = 10

degrees of freedom, df = n - 1 = 9

Given CI level is 90%, hence α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.833

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))

CI = (12 - 1.833 * 0.4397/sqrt(10) , 12 + 1.833 *
0.4397/sqrt(10))

CI = (11.75 , 12.25)

b)

Given CI level is 95%, hence α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.262

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))

CI = (12 - 2.262 * 0.4397/sqrt(10) , 12 + 2.262 *
0.4397/sqrt(10))

CI = (11.69 , 12.31)

c)

Given CI level is 99%, hence α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 3.25

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))

CI = (12 - 3.25 * 0.4397/sqrt(10) , 12 + 3.25 *
0.4397/sqrt(10))

CI = (11.55 , 12.45)

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. 11.8 11.6 11.9 11.9
12.5 11.4 12.0 11.7 11.8 11.8

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. 11.9 11.6 11.9 12.4
12.5 11.4 12.0 11.7 11.8 11.9?

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. 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...

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. 13.1 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. 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...

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

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?

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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