Confidence Intervals and Regression - AP Statistics
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Which of the following statements are correct about confidence intervals?
Which of the following statements are correct about confidence intervals?
Larger samples give narrower intervals. We are able to estimate a population proportion more precisely with a larger sample size.
As the confidence level increases the width of the confidence interval also increases. A larger confidence level increases the chance that the correct value will be found in the confidence interval. This means that the interval is larger.
Larger samples give narrower intervals. We are able to estimate a population proportion more precisely with a larger sample size.
As the confidence level increases the width of the confidence interval also increases. A larger confidence level increases the chance that the correct value will be found in the confidence interval. This means that the interval is larger.
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You are asked to create a 
confidence interval with a margin of error no larger than 
while sampling from a normally distributed population with a standard deviation of 
. What is the minimum required sample size?
You are asked to create a
Keep in mind that the margin of error for a confidence interval based on a normal population is equal to 
, where 
is the 
-score corresponding to the desired confidence level.
From the problem, we can tell that 
and 
. We can then solve for 
algebraically:
The minimum sample size is 
rounded up, which is 
. If you are unsure on problems like these, you can check the margin of error for your answer rounded down and then rounded up (in this case, for 
and 
.)
Keep in mind that the margin of error for a confidence interval based on a normal population is equal to
From the problem, we can tell that
The minimum sample size is
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Jim calculated a 
confidence interval for the mean height in inches of boys in his high school. He is not sure how to interpret this interval. Which of the following explains the meaning of 
confidence.
Jim calculated a
95% confidence means that the methods Jim uses to calculate his confidence interval give him correct results 95% of the time. It does not mean that there is a 95% chance that the true mean will be inside the interval. It also does not mean that 95% of all heights or possible sample means fall within the interval.
95% confidence means that the methods Jim uses to calculate his confidence interval give him correct results 95% of the time. It does not mean that there is a 95% chance that the true mean will be inside the interval. It also does not mean that 95% of all heights or possible sample means fall within the interval.
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The number of hamburgers served by McGregors per day is normally distributed and has a mean of 
hamburgers and a standard deviation of 
Find the range of customers served on the middle 
percent of days.
The number of hamburgers served by McGregors per day is normally distributed and has a mean of
First, find the first quartile of the distribution.
Then, find the third quartile of the distribution.
First, find the first quartile of the distribution.
Then, find the third quartile of the distribution.
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You estimate a regression model with 
and 
, where 
is the beta coefficient and 
is the standard error. Construct 95% confidence intervals for 
.
You estimate a regression model with
To construct 95% confidence intervals for 
, we simply take the coefficient and add/subtract 
. This is because 
is assumed to follow a symmetrical distribution (the normal), and 95% of the values in the sampling distribution are contained within 1.96 standard errors of 
.
To construct 95% confidence intervals for
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