Question

Confidence intervals seek to estimate a population parameter with an interval of values calculated from an observed sample statistic. Demonstrate that you understand this concept by describing a situation in which one could use a sample mean or sample proportion to produce a confidence interval as an estimate of a population mean or population proportion. I am asking you to make up a situation where a confidence interval might be computed. Clearly identify the population, sample, parameter, and statistic involved in your example. Choose an appropriate confidence level and compute the interval. Do not use any example that appeared in your book or in class. The population is (describe what the population is, in words) The sample is (describe what the sample is, in words) In my example, I am computing a confidence interval for a The parameter is (describe in words) The statistic is (describe in words, and assign a value to the statistic) The % confidence interval is from to . Finally, explain what this confidence interval means in the context of your example.

Answer #1

(a) Situation:

The mean score of a random sample of 60 students is 145 with SD of 40. To find the 95% confidence limits for the population mean.

(b) Population:

All the students of the College

(c) Sample:

sample of 65 students

(d)

Parameter:

mean score of all students of the College

(e) Statistic:

mean score of 60 students

(f) Confidence level:

= 0.05

(g)

n = 60

= 145

s = 40

95% Confidence interval:

= (134.88,155.12)

Summary:

(i) Population is: score of all students of the college

(ii) Sample is : score of 60 students

(iii) In my example, I am computing a confidence interval for average score of students of the college

(iv) The % confidence interval is from : 1.34 % to 1.55 %

(v) EXPLANATION: If repeated samples are taken and the 95% confidence interval is computed for each sample, 95% of the intervals will contain the population mean.

A confidence interval estimate of a population parameter
contains the unlikely values of that parameter.
True
False

True or False:
1. A confidence interval is used for estimating a population
parameter.
2. A confidence interval always captures the sample
statistic.
3. A confidence interval always captures the population
parameter.
4. When constructing a confidence intervals we should always use
Z-critical values.
5. The margin of error determines the center location of the
confidence interval.
6. In general, we would like to have a precise confidence
interval while having a high level of confidence.

For this term, we will create confidence intervals to estimate a
population value using the general formula:
sample estimator +/- (reliability factor)(standard error
of the estimator)
Recall that the (reliability factor) x (standard error of the
estimator)= margin of error (ME) for the interval.
The ME is a measure of the uncertainty in our estimate of the
population parameter. A confidence interval has a width=2ME.
A 95% confidence interval for the unobserved population
mean(µ), has a confidence level =
1-α...

A 99% confidence interval estimate of the population mean ? can
be interpreted to mean:
a) if all possible sample are taken and confidence intervals
created, 99% of them would include the true population mean
somewhere within their interval.
b) we have 99% confidence that we have selected a sample whose
interval does include the population mean.
c) we estimate that the population mean falls between the lower
and upper confidence limits, and this type of estimator is correct
99%...

Find a 90% confidence interval for a population mean ?
for these values. (Round your answers to three decimal places.)
(a)
n = 130, x = 0.85, s2 =
0.084
to
(b)
n = 40, x = 20.1, s2 =
3.86
to
(c)
Interpret the intervals found in part (a) and part (b).
There is a 10% chance that an individual sample proportion will
fall within the interval.In repeated sampling, 10% of all intervals
constructed in this manner will enclose...

Find a 90% confidence interval for a population mean ?
for these values. (Round your answers to three decimal places.)
(a)
n = 145, x = 0.88, s2 =
0.084
to
(b)
n = 70, x = 25.6, s2 =
3.49
to
(c)
Interpret the intervals found in part (a) and part (b).
There is a 10% chance that an individual sample proportion will
fall within the interval.There is a 90% chance that an individual
sample proportion will fall within...

Determine the margin of error for a confidence interval to
estimate the population proportion for the following confidence
levels with a sample proportion equal to 0.35 and n= 120
the margin of error for a confidence interval to estimate the
population portion for 90% confidence level is
the margin of error for a confidence interval to estimate the
population portion for 95% confidence level is
the margin of error for a confidence interval to estimate the
population portion for 97%...

Find an example of a confidence interval for a proportion in the
media or scholarly literature (do not use a statistics textbook or
website/article that is teaching or demonstrating statistics to
find the example).
At the very least it must include either the lower and upper
bounds or a point estimate with a margin of error. Make sure you
have a Proportion confidence interval and NOT a CI for the mean,
odds ratio, hazard ratio, or relative risk as these...

The sample mean always lies at the center of the
confidence interval for the true population mean ( µX
).
The sample mean is also known as the best point estimate
for µX .
The true population mean is always in a 90% confidence
interval for µX .
If one-hundred (100) 95% confidence intervals for µX are
created from some population, the true population mean is likely to
be in approximately 95 of these 100 confidence
intervals.

Consider the following situation . . .
Matilda has constructed three confidence intervals, all from the
same random sample. The confidence levels are 95%, 98%, and 99.9%.
The confidence intervals are 6.4 < μ < 12.3, 5.1
< μ < 13.6, and 6.8 < μ < 11.9.
Unfortunately, Matilda has forgotten which confidence interval goes
with which level. Match each confidence interval with its
level.
Write a post for the discussion board that indicates which
confidence interval goes with each...

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