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8.1 Confidence Intervals: The Basics
Read page 469~470
What is a point estimate?
Why is it called a point estimate?
What is a confidence interval?
How do you interpret a confidence interval?
According to a Gallup poll published on January 9, 2013, a 95% confidence interval for the true proportion of
American adults who support the death penalty is 63% ± 4%. This estimate was based on a random sample of
1038 American adults. Interpret this interval in context.
What is the margin of error?
Why do we include margin of error?
How do you interpret confidence level? In other words, what does it mean to be 95% confident?
Read “Do You Use Twitter?” on page 476
Alternate Example: According to www.gallup.com in December 2012, the Americans spent an average of $83
per day in stores, online, and in restaurants. This estimate was based on a random sample of 13, 217 adults and
has a margin of error of ± $4 with 95% confidence.
a. What is the name for the value of $83?
b. Interpret the confidence interval in context.
c. Interpret the confidence level.
Read page 476~478
What is the formula for calculating a confidence interval?
Is this formula included on the formula sheet for the AP exam?
How can we reduce the margin of error in a confidence interval?
Why do we want a small margin of error?
In a 2009 survey, researchers asked random sample of US teens and adults if they use social networking sites.
Overall, 73% of the teens said yes and 47% of the adults said yes. A 90% confidence interval for the true
difference in the proportion of teens and adults who would say yes is 0.229 to 0.291.
a. Interpret the confidence level.
b. Interpret the confidence interval.
c. Based on the interval, is there convincing evidence that the proportion of teens who would say yes is higher
than the proportion of adults who would say yes? Explain.
d. How would the interval be affected if we used a 99% confidence level instead of a 90% confidence level?
8.3 Confidence Intervals:
Read page 501~510
When should we use a t* critical value rather than a z* critical value for calculating a CI for a population mean?
How do we calculate the value of t* ?
How do we calculate degree of freedom?
What is a t distribution? Describe the shape, center, and spread of the t distribution.
Suppose you wanted to construct a 90% confidence interval for µ using a sample size of a Normal population
based on an SRS of size 10. What critical value of t* should you use?
What if you wanted to construct a 99% confidence interval for µ using a sample size of 75?
What is the formula for the standard error of the sample mean?
How do you interpret this value?
What is the formula for a confidence interval for a population mean?
What are the three conditions for constructing a confidence interval for a population mean?
How Much Homework?
The principal at a large high school claims that students at his school spend at least 10 hours per week doing
homework, on average. To investigate this claim, an AP Statistics class selected a random sample of 250
students from their school and asked them how long they spent doing homework during the last week. The
sample mean was 10.2 hours and the sample standard deviation was 4.2 hours.
Construct and interpret a 95% confidence interval for the mean time that all students at this school spent doing
homework in the last week.
Based on your interval from part (a), what can you conclude about the principal’s claim?
Read page 511~
The Normal condition: What if the sample size is small l(n<30) and we don’t know the shape of the
population?
How can you lose credit for the Normal condition on the AP Exam?