Asked by triciabeesley1011 Image transcription text Construct a 90% confidence interval of the population proportion using the given information. x = 45, n = 150 Click here to view the table of critical values. The lower bound is i
Table of critical values X The upper bound is (Round to three decimal places as needed.) Level of Confidence, Area in Each Tail, NIR Critical Value, z (1 - a) . 100% 90% 0.05 1.645 95% 0.025 1.96 99% 0.005 2.575 Print Done Enter your answer in each of the answer boxes.
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Terms in this set (19)
A ________ ________ is the value of a statistic that estimates the value of a parameter.
point estimate
The _______ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. It is denoted _______.
level of confidence, (1-a)*100%
Compute the critical value
zα/2
that corresponds to a 80% level of confidence.
zα/2=1.28
(Round to two decimal places as needed.)
Determine the point estimate of the population proportion, the margin of error for the following confidence interval,
and the number of individuals in the sample with the specified characteristic, x, for the sample size provided.
Lower bound=0.121, upper bound=0.639, n=1200
The point estimate of the population proportion is 0.38.
(Round to the nearest thousandth as needed.)
The margin of error is 0.259.
(Round to the nearest thousandth as needed.)
The number of individuals in the sample with the specified characteristic is 456.
(Round to the
nearest integer as needed.)
Construct a 95% confidence interval of the population proportion using the given information.
x=175, n=250
The lower bound is 0.643
The upper bound is 0.757
(Round to three decimal places as needed.)
(a) We are 95% confident 66% of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.
The interpretation is flawed. The interpretation provides no interval about the population proportion.
(b) We are 91% to 99% confident 66% of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.
The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
(c) We are 95%
confident that the interval from
0.62 to 0.70contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low.
The interpretation is reasonable.
(d) In 95% of samples of adults in the country during the period of economic uncertainty, the proportion who believed wages paid to workers in industry were too low is between 0.62 and 0.70.
The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true.
A survey of 2322 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 422 have donated blood in the past two years. Complete parts (a) through (c) below.
(a) Obtain a point estimate for the population proportion of adults in the country aged 18 and older who have donated blood in the past two years.
(b) Verify that the requirements for constructing a confidence interval about p are satisfied.
(c) Construct and interpret a 90% confidence interval for the population proportion of adults in the country who have donated blood in the past two years. Select the correct choice
below and fill in any answer boxes within your choice.
(Type integers or decimals rounded to three decimal places as needed. Use ascending order.)
a) p-head = 0.182
b) The sample can be assumed to be a simple random sample, the value of np(1-p) is 345.69, which is greater than or equal to 10, and the sample size can be assumed to be less than or equal to 5% of the population size. (Round to three decimal places as needed.)
c) We are 90% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between 0.169 (upper bound)and 0.195(lower bound).
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 95% confidence if
(a) she uses a previous estimate of 0.38?
(b) she does not use any
prior estimates?
a) n= 1006
b) n= 1068
Explain what
"95%
confidence" means in a
95%
confidence interval.
if 100 different confidence intervals are constructed, each based on a different sample of size n from the same population, then we expect
95
of the intervals to include the parameter and
5
to not include the parameter.
By how many times does the sample size have to be increased to decrease the margin of error by a factor of
1/9?
The sample size must be increased by a factor of 8181 to decrease the margin of error by a factor of 1/9.
(Type a whole number.)
Increasing the sample size by a factor M results in the margin of error decreasing by a factor of
1/sqrt(M).
Two
researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-handed. They find the point estimate is
0.08.
Each independently constructed a confidence interval based on the point estimate, but Jaime's interval has a lower bound of
0.011
and an upper bound of
0.149,
while Mariya's interval has a lower bound of
0.059
and an upper bound of
0.163.
Which interval is wrong? Why?'s
interval is
wrong because it is not centered on the point estimate.
Mariya's
interval is wrong because it is not centered on the point estimate.
Determine whether the following statement is true or false.
To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal.
This statement is false
Fill in the blank in the statement below.
The procedure for constructing a confidence interval about a mean is _______, which means minor departures from normality do not affect the accuracy of the interval.
robust,
The data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation
coefficient of 0.945.
Judge whether a t-interval could be constructed using the data in the sample.
The normal probability plot does not suggest the data could come from a normal population because 0.945less than<0.959 and the boxplot shows outliers, so a t-interval could not be constructed.
(Round to three decimal places as needed.)
Determine the point estimate of the population mean and margin of
error for the confidence interval.
Lower bound is 19, upper bound is 27.
Determine the point estimate of the population mean and margin of error for the confidence interval.
Lower bound is 19, upper bound is 27.
The point estimate of the population mean is 23(19+27)/2.
The margin of error for the confidence interval is 4(27-19)/2.
In a survey conducted by the Gallup Organization, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5. Provide two recommendations for decreasing the margin of error of the interval.
Increase the sample size.
Decrease the confidence level.
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