Confidence Intervals: The Basics BPS chapter 14

Confidence Intervals: The
Basics
BPS chapter 14
© 2006 W.H. Freeman and Company
Statistical Inference
What is statistical inference on ?
a)
b)
c)
d)
Drawing conclusions about a population mean based on information
contained in a sample.
Drawing conclusions about a sample mean based on information
contained in a population.
Drawing conclusions about a sample mean based on the
measurements in that sample.
Selecting a set of data from a large population.
Statistical Inference (answer)
What is statistical inference on ?
a)
b)
c)
d)
Drawing conclusions about a population mean based on
information contained in a sample.
Drawing conclusions about a sample mean based on information
contained in a population.
Drawing conclusions about a sample mean based on the
measurements in that sample.
Selecting a set of data from a large population.
Inference
The conditions for doing inference on  using the standard normal
distribution do NOT include:
a)
b)
c)
d)
A simple random sample of size n.
A normal population or sample size large enough to apply the
Central Limit Theorem.
A known value of .
A known value of .
Inference (answer)
The conditions for doing inference on  using the standard normal
distribution do NOT include:
a)
b)
c)
d)
A simple random sample of size n.
A normal population or sample size large enough to apply the
Central Limit Theorem.
A known value of .
A known value of .
Inference
Why do we need a normal population or large sample size to do
inference on ?
a)
b)
c)
d)
So that the sampling distribution of x is normal or approximately
normal.
So that the distribution of the sample data is normal or
approximately normal.
So that x equals .
So that  is known.
Inference (answer)
Why do we need a normal population or large sample size to do
inference on ?
a)
b)
c)
d)
So that the sampling distribution of x is normal or
approximately normal.
So that the distribution of the sample data is normal or
approximately normal.
So that x equals .
So that  is known.
Inference
True or False: The condition of known  is often met even when  is
unknown.
a)
b)
True
False
Inference (answer)
True or False: The condition of known  is often met even when  is
unknown.
a)
b)
True
False
Confidence Intervals
The purpose of a confidence interval for  is
a)
b)
c)
d)
To give a range of reasonable values for the level of confidence.
To give a range of reasonable values for the sample mean.
To give a range of reasonable values for the population mean.
To give a range of reasonable values for the difference between the
sample mean and the population mean.
Confidence Intervals (answer)
The purpose of a confidence interval for  is
a)
b)
c)
d)
To give a range of reasonable values for the level of confidence.
To give a range of reasonable values for the sample mean.
To give a range of reasonable values for the population mean.
To give a range of reasonable values for the difference between the
sample mean and the population mean.
Confidence intervals
The confidence interval formula for  does NOT include
a)
b)
c)
d)
e)
f)
The sample mean.
The population standard deviation.
The z* value for specified level of confidence.
The margin of error.
The sample size.
The population size.
Confidence intervals (answer)
The confidence interval formula for  does NOT include
a)
b)
c)
d)
e)
f)
The sample mean.
The population standard deviation.
The z* value for specified level of confidence.
The margin of error.
The sample size.
The population size.
Confidence intervals
What do we hope to capture within a confidence interval?
a)
b)
c)
d)
e)
f)
The unknown confidence level.
The unknown parameter.
The unknown statistic.
The parameter estimate.
The margin of error.
The sample size.
Confidence intervals (answer)
What do we hope to capture within a confidence interval?
a)
b)
c)
d)
e)
f)
The unknown confidence level.
The unknown parameter.
The unknown statistic.
The parameter estimate.
The margin of error.
The sample size.
Confidence intervals
What are the three components of a confidence interval?
a)
b)
c)
Estimate of confidence level, sample size, and margin of error.
Mean of sample statistic, confidence level, and margin of error.
Estimate of population parameter, confidence level, and margin of
error.
Confidence intervals (answer)
What are the three components of a confidence interval?
a)
b)
c)
Estimate of confidence level, sample size, and margin of error.
Mean of sample statistic, confidence level, and margin of error.
Estimate of population parameter, confidence level, and margin
of error.
Confidence intervals
Consider the following statement.
“We are 90% confident that the population mean is between 344.8 and
361.2 pounds.”
Which of the following statements about this confidence interval
interpretation is valid?
a)
b)
c)
d)
This interpretation is incorrect because there is no statement of the
true parameter in words.
This interpretation is incorrect because the interval is not reported.
This interpretation is incorrect because the confidence level is not
reported.
This is a correct reporting of the confidence interval.
Confidence intervals (answer)
Consider the following statement.
“We are 90% confident that the population mean is between 344.8 and
361.2 pounds.”
Which of the following statements about this confidence interval
interpretation is valid?
a)
b)
c)
d)
This interpretation is incorrect because there is no statement
of the true parameter in words.
This interpretation is incorrect because the interval is not reported.
This interpretation is incorrect because the confidence level is not
reported.
This is a correct reporting of the confidence interval.
Confidence intervals
Consider the following statement.
“The average time a local company takes to process new insurance
claims is 9 to 11 days.”
Which of the following statements about this confidence interval
interpretation is valid?
a)
b)
c)
d)
This interpretation is incorrect because there is no statement of the
true parameter in words.
This interpretation is incorrect because the interval is not reported.
This interpretation is incorrect because the confidence level is not
reported.
This is a correct reporting of the confidence interval.
Confidence intervals (answer)
Consider the following statement.
“The average time a local company takes to process new insurance
claims is 9 to 11 days.”
Which of the following statements about this confidence interval
interpretation is valid?
a)
b)
c)
d)
This interpretation is incorrect because there is no statement of the
true parameter in words.
This interpretation is incorrect because the interval is not reported.
This interpretation is incorrect because the confidence level is
not reported.
This is a correct reporting of the confidence interval.
Confidence intervals
Consider the following statement.
“With 95% confidence, the mean sodium content for beef hotdogs is
between 353.2 and 449.1 mg.”
Which of the following statements about this confidence interval
interpretation is valid?
a)
b)
c)
d)
This interpretation is incorrect because there is no statement of the
true parameter in words.
This interpretation is incorrect because the interval is not reported.
This interpretation is incorrect because the confidence level is not
reported.
This is a correct reporting of the confidence interval.
Confidence intervals (answer)
Consider the following statement.
“With 95% confidence, the mean sodium content for beef hotdogs is
between 353.2 and 449.1 mg.”
Which of the following statements about this confidence interval
interpretation is valid?
a)
b)
c)
d)
This interpretation is incorrect because there is no statement of the
true parameter in words.
This interpretation is incorrect because the interval is not reported.
This interpretation is incorrect because the confidence level is not
reported.
This is a correct reporting of the confidence interval.
Confidence intervals
Consider the following statement.
“With 99% confidence, the average time it takes passengers of a local
airline to claim their luggage is 25 minutes.”
Which of the following statements about this confidence interval
interpretation is valid?
a)
b)
c)
d)
This interpretation is incorrect because there is no statement of the
true parameter in words.
This interpretation is incorrect because the interval is not reported.
This interpretation is incorrect because the confidence level is not
reported.
This is a correct reporting of the confidence interval.
Confidence intervals (answer)
Consider the following statement.
“With 99% confidence, the average time it takes passengers of a local
airline to claim their luggage is 25 minutes.”
Which of the following statements about this confidence interval
interpretation is valid?
a)
b)
c)
d)
This interpretation is incorrect because there is no statement of the
true parameter in words.
This interpretation is incorrect because the interval is not
reported.
This interpretation is incorrect because the confidence level is not
reported.
This is a correct reporting of the confidence interval.
Confidence intervals
A very large school district in Connecticut wants to estimate the
average SAT score of this year’s graduating class. The district
takes a simple random sample of 100 seniors and calculates the
95% confidence interval for the graduating students’ average SAT
score at 505 to 520 points.
For the sample of 100 graduating seniors, 95% of their SAT scores
were between 505 and 520 points.
a)
b)
Correct interpretation of interval.
Incorrect interpretation of interval.
Confidence intervals (answer)
A very large school district in Connecticut wants to estimate the
average SAT score of this year’s graduating class. The district
takes a simple random sample of 100 seniors and calculates the
95% confidence interval for the graduating students’ average SAT
score at 505 to 520 points.
For the sample of 100 graduating seniors, 95% of their SAT scores
were between 505 and 520 points.
a)
b)
Correct interpretation of interval.
Incorrect interpretation of interval.
Confidence intervals
A very large school district in Connecticut wants to estimate the
average SAT score of this year’s graduating class. The district
takes a simple random sample of 100 seniors and calculates the
95% confidence interval for the graduating students’ average SAT
score at 505 to 520 points.
The school district can be 95% confident that the mean SAT score of
the 100 students is contained in the interval of 505 to 520 points.
a)
b)
Correct interpretation of interval.
Incorrect interpretation of interval.
Confidence intervals (answer)
A very large school district in Connecticut wants to estimate the
average SAT score of this year’s graduating class. The district
takes a simple random sample of 100 seniors and calculates the
95% confidence interval for the graduating students’ average SAT
score at 505 to 520 points.
The school district can be 95% confident that the mean SAT score of
the 100 students is contained in the interval of 505 to 520 points.
a)
b)
Correct interpretation of interval.
Incorrect interpretation of interval.
Confidence intervals
A very large school district in Connecticut wants to estimate the
average SAT score of this year’s graduating class. The district
takes a simple random sample of 100 seniors and calculates the
95% confidence interval for the graduating students’ average SAT
score at 505 to 520 points.
The interval of 505 to 520 points gives a range of reasonable values for
the true average SAT score of the graduating students in the large
Connecticut school district. The school district can be 95%
confident this interval captures their graduating students’ average
SAT score.
a)
b)
Correct interpretation of interval.
Incorrect interpretation of interval.
Confidence intervals (answer)
A very large school district in Connecticut wants to estimate the
average SAT score of this year’s graduating class. The district
takes a simple random sample of 100 seniors and calculates the
95% confidence interval for the graduating students’ average SAT
score at 505 to 520 points.
The interval of 505 to 520 points gives a range of reasonable values for
the true average SAT score of the graduating students in the large
Connecticut school district. The school district can be 95%
confident this interval captures their graduating students’ average
SAT score.
a)
b)
Correct interpretation of interval.
Incorrect interpretation of interval.
Confidence intervals
A very large school district in Connecticut wants to estimate the
average SAT score of this year’s graduating class. The district
takes a simple random sample of 100 seniors and calculates the
95% confidence interval for the graduating students’ average SAT
score at 505 to 520 points.
The probability that the interval of 505 to 520 points captures the large
Connecticut school district’s graduating seniors’ average SAT score
is 0.95.
a)
b)
Correct interpretation of interval.
Incorrect interpretation of interval.
Confidence intervals (answer)
A very large school district in Connecticut wants to estimate the
average SAT score of this year’s graduating class. The district
takes a simple random sample of 100 seniors and calculates the
95% confidence interval for the graduating students’ average SAT
score at 505 to 520 points.
The probability that the interval of 505 to 520 points captures the large
Connecticut school district’s graduating seniors’ average SAT score
is 0.95.
a)
b)
Correct interpretation of interval.
Incorrect interpretation of interval.
Confidence intervals
The probability that a 90% confidence interval for a population mean
captures  is
a)
b)
c)
d)
0.
0.90.
1.
Either 0 or 1—we do not know which.
Confidence intervals (answer)
The probability that a 90% confidence interval for a population mean
captures  is
a)
b)
c)
d)
0.
0.90.
1.
Either 0 or 1—we do not know which.
Confidence intervals
What is the confidence level in a confidence interval for ?
a)
b)
c)
The percentage of confidence intervals produced by the procedure
that contain .
The probability that a specific confidence interval contains .
The percentage of confidence interval procedures that will create an
interval that contains .
Confidence intervals (answer)
What is the confidence level in a confidence interval for ?
a)
b)
c)
The percentage of confidence intervals produced by the
procedure that contain .
The probability that a specific confidence interval contains .
The percentage of confidence interval procedures that will create an
interval that contains .
Margin of error
Increasing the confidence level will
a)
b)
Increase the margin of error.
Decrease the margin of error.
Margin of error (answer)
Increasing the confidence level will
a)
b)
Increase the margin of error.
Decrease the margin of error.
Margin of error
Increasing the sample size will
a)
b)
Increase the margin of error.
Decrease the margin of error.
Margin of error (answer)
Increasing the sample size will
a)
b)
Increase the margin of error.
Decrease the margin of error.
Margin of error
Increasing the standard deviation will
a)
b)
Increase the margin of error.
Decrease the margin of error.
Margin of error (answer)
Increasing the standard deviation will
a)
b)
Increase the margin of error.
Decrease the margin of error.
Margin of error
Which of the following components of the margin of error in a
confidence interval for  does a researcher NOT have the chance to
select?
a)
b)
c)
Confidence level.
Sample size.
Population standard deviation.
Margin of error (answer)
Which of the following components of the margin of error in a
confidence interval for  does a researcher NOT have the chance to
select?
a)
b)
c)
Confidence level.
Sample size.
Population standard deviation.