AP Statistics
Clifton Chapter 9 Notes Estimation Using a Single Sample
Section 9.1 – Point Estimation What is a point estimate and what is its purpose?
• Choosing a Statistic for Computing an Estimate There are three sampling distributions in Figure 9.1. What two attributes make (c) the most desirable statistic to use as a point estimate?
What is meant by the term “unbiased” statistic?
How does one choose an unbiased statistic for estimating ߤ when a population is normal? Not Normal?
Exercises # 1, 2, 3, 4, 5, 6, 7, 8 Section 9.2 – Large-Sample Confidence Interval for a Population Proportion Why might a confidence interval be preferred to a point estimate?
What does the confidence level represent and how is it based on long run success?
What is meant by “large-sample” confidence interval for p?
What are three justifications for using a large-sample confidence interval for p? 1. 2. 3.
AP Statistics
Clifton
Describe how the construction of a confidence interval is based on the sampling distribution for a point estimate. Include a discussion of how z*(the z critical value) is computed:
The following questions refer to Figure 9.4 and accompanying text: How many intervals are there? Why do they all have the same width? Why don’t the intervals line up exactly? Where are they the most concentrated? How many contain the true population proportion? Why is it incorrect to say that the confidence level of 95% represents the probability that p is in the interval?
To what does the 95% refer?
Comment on the use of the word “approximately” in the following interpretation of confidence level: Of 100 intervals constructed in this manner, approximately 95 of them will contain the true proportion.
What is the trade-off between confidence level and width of the interval? Use the words “reliability” and “precision” in your response.
Note: The text offers an alternative to the large-sample z interval that goes beyond the scope of the AP Statistics syllabus. For those students preparing for the AP exam, the only confidence interval constructed for p (population proportion) is a z interval.
AP Statistics
•
Clifton
General Form of Confidence Interval
Write down the general form of a confidence interval and define each of its parts:
What is meant by the standard error of a statistic and how is it calculated for p?
What does the bound on the error of estimation represent and how is it calculated?
Note that the text uses 95% in its definition of error bound. How would the calculation change if 90% were used? 98%?
•
Choosing the Sample Size
Starting with the given formula for error bound, B, use algebra to solve for sample size, n:
In determining sample size for a given error bound, what value is used for ߨ when information is limited or a conservatively large value is desired?
Exercises # 10, 11, 12, 13, 16, 17, 18, 19, 21, 23, 25, 33 Section 9.3 – Confidence Interval for a Population Mean Describe the construction of a z confidence interval for ߤ when sigma is known. Be sure to define each element of the formula:
How does sample size n affect the justification for using a z interval?
Under what conditions can the z interval formula be used when n is small (n30)?
AP Statistics
•
Clifton
Confidence Interval for ࣆ When ࣌ Is Unknown
Review the steps for creating a z confidence interval for ߤ when ߪ is known. What important aspect of that process changes when ߪ is unknown?
•
T Distributions
Refer to the “Important Properties of t Distributions” for the following questions: In what ways are t distributions similar to the normal distributions?
How are they different from the normal distributions?
•
One-Sample t Confidence Interval
Compare the calculation of the z to the formula for computing t. How are they similar?
What statistic is used in place of ߪ?
Describe the effect on the width of the interval when using t rather than z:
Discuss the similarities and differences in the steps for constructing a one-sample t confidence interval for ߤ to that of creating a z interval for ߤ:
AP Statistics
Clifton
What is the limitation placed upon using a t interval for sample sizes smaller than 30 and how might that condition be checked?
•
Choosing the Sample Size
Discuss the effect of ߪ and B on the computed sample size, n:
What is the recommendation for rounding the final calculation of sample size?
Exercises # 34, 35, 36, 37, 40, 41, 43, 45, 48, 52 Section 9.4 – Interpreting and Communicating Results of Statistical Analysis •
Communicating the Results of a Statistical Analysis
Read Example 9.5 Dangerous Driving and pay attention to the way the conclusion is stated. The conclusion contains the following elements: level of confidence (90%), the name of the characteristic in context (the true proportion of drivers who have engaged in careless or aggressive driving in the past six months), and the bounds of the interval (between .885 and .915). Note: Every time you construct a confidence interval, the conclusion should be stated in this manner. Now work problem 9.15 at the end of this section. Practice writing a conclusion for that problem incorporating the elements listed above: Based on these sample data, we can be _____ % confident that the true _____________ of ____________________________ who ________________________________ is between __________ and ______________. In addition, write a statement that is an interpretation of the level of confidence for that problem:
AP Statistics
•
Interpreting the Results of a Statistical Analysis
Describe some of the methods used in the articles to report margin of error:
•
What to Look For in Published Data
Outline the questions you should ask when reading research reports: 1. 2. 3.
•
A Word to the Wise: Cautions and Limitations
Briefly summarize the issues that should be addressed when working with confidence interval estimates: 1. 2. 3. 4. Exercises # 53, 54, 55, 63, 66, 68, 74
Clifton
AP Statistics
Clifton Chapter 9 Notes Estimation Using a Single Sample
Section 9.1 – Point Estimation What is a point estimate and what is its purpose?
• Choosing a Statistic for Computing an Estimate There are three sampling distributions in Figure 9.1. What two attributes make (c) the most desirable statistic to use as a point estimate?
What is meant by the term “unbiased” statistic?
How does one choose an unbiased statistic for estimating ߤ when a population is normal? Not Normal?
Exercises # 1, 2, 3, 4, 5, 6, 7, 8 Section 9.2 – Large-Sample Confidence Interval for a Population Proportion Why might a confidence interval be preferred to a point estimate?
What does the confidence level represent and how is it based on long run success?
What is meant by “large-sample” confidence interval for p?
What are three justifications for using a large-sample confidence interval for p? 1. 2. 3.
AP Statistics
Clifton
Describe how the construction of a confidence interval is based on the sampling distribution for a point estimate. Include a discussion of how z*(the z critical value) is computed:
The following questions refer to Figure 9.4 and accompanying text: How many intervals are there? Why do they all have the same width? Why don’t the intervals line up exactly? Where are they the most concentrated? How many contain the true population proportion? Why is it incorrect to say that the confidence level of 95% represents the probability that p is in the interval?
To what does the 95% refer?
Comment on the use of the word “approximately” in the following interpretation of confidence level: Of 100 intervals constructed in this manner, approximately 95 of them will contain the true proportion.
What is the trade-off between confidence level and width of the interval? Use the words “reliability” and “precision” in your response.
Note: The text offers an alternative to the large-sample z interval that goes beyond the scope of the AP Statistics syllabus. For those students preparing for the AP exam, the only confidence interval constructed for p (population proportion) is a z interval.
AP Statistics
•
Clifton
General Form of Confidence Interval
Write down the general form of a confidence interval and define each of its parts:
What is meant by the standard error of a statistic and how is it calculated for p?
What does the bound on the error of estimation represent and how is it calculated?
Note that the text uses 95% in its definition of error bound. How would the calculation change if 90% were used? 98%?
•
Choosing the Sample Size
Starting with the given formula for error bound, B, use algebra to solve for sample size, n:
In determining sample size for a given error bound, what value is used for ߨ when information is limited or a conservatively large value is desired?
Exercises # 10, 11, 12, 13, 16, 17, 18, 19, 21, 23, 25, 33 Section 9.3 – Confidence Interval for a Population Mean Describe the construction of a z confidence interval for ߤ when sigma is known. Be sure to define each element of the formula:
How does sample size n affect the justification for using a z interval?
Under what conditions can the z interval formula be used when n is small (n30)?
AP Statistics
•
Clifton
Confidence Interval for ࣆ When ࣌ Is Unknown
Review the steps for creating a z confidence interval for ߤ when ߪ is known. What important aspect of that process changes when ߪ is unknown?
•
T Distributions
Refer to the “Important Properties of t Distributions” for the following questions: In what ways are t distributions similar to the normal distributions?
How are they different from the normal distributions?
•
One-Sample t Confidence Interval
Compare the calculation of the z to the formula for computing t. How are they similar?
What statistic is used in place of ߪ?
Describe the effect on the width of the interval when using t rather than z:
Discuss the similarities and differences in the steps for constructing a one-sample t confidence interval for ߤ to that of creating a z interval for ߤ:
AP Statistics
Clifton
What is the limitation placed upon using a t interval for sample sizes smaller than 30 and how might that condition be checked?
•
Choosing the Sample Size
Discuss the effect of ߪ and B on the computed sample size, n:
What is the recommendation for rounding the final calculation of sample size?
Exercises # 34, 35, 36, 37, 40, 41, 43, 45, 48, 52 Section 9.4 – Interpreting and Communicating Results of Statistical Analysis •
Communicating the Results of a Statistical Analysis
Read Example 9.5 Dangerous Driving and pay attention to the way the conclusion is stated. The conclusion contains the following elements: level of confidence (90%), the name of the characteristic in context (the true proportion of drivers who have engaged in careless or aggressive driving in the past six months), and the bounds of the interval (between .885 and .915). Note: Every time you construct a confidence interval, the conclusion should be stated in this manner. Now work problem 9.15 at the end of this section. Practice writing a conclusion for that problem incorporating the elements listed above: Based on these sample data, we can be _____ % confident that the true _____________ of ____________________________ who ________________________________ is between __________ and ______________. In addition, write a statement that is an interpretation of the level of confidence for that problem:
AP Statistics
•
Interpreting the Results of a Statistical Analysis
Describe some of the methods used in the articles to report margin of error:
•
What to Look For in Published Data
Outline the questions you should ask when reading research reports: 1. 2. 3.
•
A Word to the Wise: Cautions and Limitations
Briefly summarize the issues that should be addressed when working with confidence interval estimates: 1. 2. 3. 4. Exercises # 53, 54, 55, 63, 66, 68, 74
Clifton
AP Statistics
Clifton Chapter 9 Notes Estimation Using a Single Sample
Section 9.1 – Point Estimation What is a point estimate and what is its purpose?
• Choosing a Statistic for Computing an Estimate There are three sampling distributions in Figure 9.1. What two attributes make (c) the most desirable statistic to use as a point estimate?
What is meant by the term “unbiased” statistic?
How does one choose an unbiased statistic for estimating ߤ when a population is normal? Not Normal?
Exercises # 1, 2, 3, 4, 5, 6, 7, 8 Section 9.2 – Large-Sample Confidence Interval for a Population Proportion Why might a confidence interval be preferred to a point estimate?
What does the confidence level represent and how is it based on long run success?
What is meant by “large-sample” confidence interval for p?
What are three justifications for using a large-sample confidence interval for p? 1. 2. 3.
AP Statistics
Clifton
Describe how the construction of a confidence interval is based on the sampling distribution for a point estimate. Include a discussion of how z*(the z critical value) is computed:
The following questions refer to Figure 9.4 and accompanying text: How many intervals are there? Why do they all have the same width? Why don’t the intervals line up exactly? Where are they the most concentrated? How many contain the true population proportion? Why is it incorrect to say that the confidence level of 95% represents the probability that p is in the interval?
To what does the 95% refer?
Comment on the use of the word “approximately” in the following interpretation of confidence level: Of 100 intervals constructed in this manner, approximately 95 of them will contain the true proportion.
What is the trade-off between confidence level and width of the interval? Use the words “reliability” and “precision” in your response.
Note: The text offers an alternative to the large-sample z interval that goes beyond the scope of the AP Statistics syllabus. For those students preparing for the AP exam, the only confidence interval constructed for p (population proportion) is a z interval.
AP Statistics
•
Clifton
General Form of Confidence Interval
Write down the general form of a confidence interval and define each of its parts:
What is meant by the standard error of a statistic and how is it calculated for p?
What does the bound on the error of estimation represent and how is it calculated?
Note that the text uses 95% in its definition of error bound. How would the calculation change if 90% were used? 98%?
•
Choosing the Sample Size
Starting with the given formula for error bound, B, use algebra to solve for sample size, n:
In determining sample size for a given error bound, what value is used for ߨ when information is limited or a conservatively large value is desired?
Exercises # 10, 11, 12, 13, 16, 17, 18, 19, 21, 23, 25, 33 Section 9.3 – Confidence Interval for a Population Mean Describe the construction of a z confidence interval for ߤ when sigma is known. Be sure to define each element of the formula:
How does sample size n affect the justification for using a z interval?
Under what conditions can the z interval formula be used when n is small (n30)?
AP Statistics
•
Clifton
Confidence Interval for ࣆ When ࣌ Is Unknown
Review the steps for creating a z confidence interval for ߤ when ߪ is known. What important aspect of that process changes when ߪ is unknown?
•
T Distributions
Refer to the “Important Properties of t Distributions” for the following questions: In what ways are t distributions similar to the normal distributions?
How are they different from the normal distributions?
•
One-Sample t Confidence Interval
Compare the calculation of the z to the formula for computing t. How are they similar?
What statistic is used in place of ߪ?
Describe the effect on the width of the interval when using t rather than z:
Discuss the similarities and differences in the steps for constructing a one-sample t confidence interval for ߤ to that of creating a z interval for ߤ:
AP Statistics
Clifton
What is the limitation placed upon using a t interval for sample sizes smaller than 30 and how might that condition be checked?
•
Choosing the Sample Size
Discuss the effect of ߪ and B on the computed sample size, n:
What is the recommendation for rounding the final calculation of sample size?
Exercises # 34, 35, 36, 37, 40, 41, 43, 45, 48, 52 Section 9.4 – Interpreting and Communicating Results of Statistical Analysis •
Communicating the Results of a Statistical Analysis
Read Example 9.5 Dangerous Driving and pay attention to the way the conclusion is stated. The conclusion contains the following elements: level of confidence (90%), the name of the characteristic in context (the true proportion of drivers who have engaged in careless or aggressive driving in the past six months), and the bounds of the interval (between .885 and .915). Note: Every time you construct a confidence interval, the conclusion should be stated in this manner. Now work problem 9.15 at the end of this section. Practice writing a conclusion for that problem incorporating the elements listed above: Based on these sample data, we can be _____ % confident that the true _____________ of ____________________________ who ________________________________ is between __________ and ______________. In addition, write a statement that is an interpretation of the level of confidence for that problem:
AP Statistics
•
Interpreting the Results of a Statistical Analysis
Describe some of the methods used in the articles to report margin of error:
•
What to Look For in Published Data
Outline the questions you should ask when reading research reports: 1. 2. 3.
•
A Word to the Wise: Cautions and Limitations
Briefly summarize the issues that should be addressed when working with confidence interval estimates: 1. 2. 3. 4. Exercises # 53, 54, 55, 63, 66, 68, 74
Clifton
AP Statistics
Clifton Chapter 9 Notes Estimation Using a Single Sample
Section 9.1 – Point Estimation What is a point estimate and what is its purpose?
• Choosing a Statistic for Computing an Estimate There are three sampling distributions in Figure 9.1. What two attributes make (c) the most desirable statistic to use as a point estimate?
What is meant by the term “unbiased” statistic?
How does one choose an unbiased statistic for estimating ߤ when a population is normal? Not Normal?
Exercises # 1, 2, 3, 4, 5, 6, 7, 8 Section 9.2 – Large-Sample Confidence Interval for a Population Proportion Why might a confidence interval be preferred to a point estimate?
What does the confidence level represent and how is it based on long run success?
What is meant by “large-sample” confidence interval for p?
What are three justifications for using a large-sample confidence interval for p? 1. 2. 3.
AP Statistics
Clifton
Describe how the construction of a confidence interval is based on the sampling distribution for a point estimate. Include a discussion of how z*(the z critical value) is computed:
The following questions refer to Figure 9.4 and accompanying text: How many intervals are there? Why do they all have the same width? Why don’t the intervals line up exactly? Where are they the most concentrated? How many contain the true population proportion? Why is it incorrect to say that the confidence level of 95% represents the probability that p is in the interval?
To what does the 95% refer?
Comment on the use of the word “approximately” in the following interpretation of confidence level: Of 100 intervals constructed in this manner, approximately 95 of them will contain the true proportion.
What is the trade-off between confidence level and width of the interval? Use the words “reliability” and “precision” in your response.
Note: The text offers an alternative to the large-sample z interval that goes beyond the scope of the AP Statistics syllabus. For those students preparing for the AP exam, the only confidence interval constructed for p (population proportion) is a z interval.
AP Statistics
•
Clifton
General Form of Confidence Interval
Write down the general form of a confidence interval and define each of its parts:
What is meant by the standard error of a statistic and how is it calculated for p?
What does the bound on the error of estimation represent and how is it calculated?
Note that the text uses 95% in its definition of error bound. How would the calculation change if 90% were used? 98%?
•
Choosing the Sample Size
Starting with the given formula for error bound, B, use algebra to solve for sample size, n:
In determining sample size for a given error bound, what value is used for ߨ when information is limited or a conservatively large value is desired?
Exercises # 10, 11, 12, 13, 16, 17, 18, 19, 21, 23, 25, 33 Section 9.3 – Confidence Interval for a Population Mean Describe the construction of a z confidence interval for ߤ when sigma is known. Be sure to define each element of the formula:
How does sample size n affect the justification for using a z interval?
Under what conditions can the z interval formula be used when n is small (n30)?
AP Statistics
•
Clifton
Confidence Interval for ࣆ When ࣌ Is Unknown
Review the steps for creating a z confidence interval for ߤ when ߪ is known. What important aspect of that process changes when ߪ is unknown?
•
T Distributions
Refer to the “Important Properties of t Distributions” for the following questions: In what ways are t distributions similar to the normal distributions?
How are they different from the normal distributions?
•
One-Sample t Confidence Interval
Compare the calculation of the z to the formula for computing t. How are they similar?
What statistic is used in place of ߪ?
Describe the effect on the width of the interval when using t rather than z:
Discuss the similarities and differences in the steps for constructing a one-sample t confidence interval for ߤ to that of creating a z interval for ߤ:
AP Statistics
Clifton
What is the limitation placed upon using a t interval for sample sizes smaller than 30 and how might that condition be checked?
•
Choosing the Sample Size
Discuss the effect of ߪ and B on the computed sample size, n:
What is the recommendation for rounding the final calculation of sample size?
Exercises # 34, 35, 36, 37, 40, 41, 43, 45, 48, 52 Section 9.4 – Interpreting and Communicating Results of Statistical Analysis •
Communicating the Results of a Statistical Analysis
Read Example 9.5 Dangerous Driving and pay attention to the way the conclusion is stated. The conclusion contains the following elements: level of confidence (90%), the name of the characteristic in context (the true proportion of drivers who have engaged in careless or aggressive driving in the past six months), and the bounds of the interval (between .885 and .915). Note: Every time you construct a confidence interval, the conclusion should be stated in this manner. Now work problem 9.15 at the end of this section. Practice writing a conclusion for that problem incorporating the elements listed above: Based on these sample data, we can be _____ % confident that the true _____________ of ____________________________ who ________________________________ is between __________ and ______________. In addition, write a statement that is an interpretation of the level of confidence for that problem:
AP Statistics
•
Interpreting the Results of a Statistical Analysis
Describe some of the methods used in the articles to report margin of error:
•
What to Look For in Published Data
Outline the questions you should ask when reading research reports: 1. 2. 3.
•
A Word to the Wise: Cautions and Limitations
Briefly summarize the issues that should be addressed when working with confidence interval estimates: 1. 2. 3. 4. Exercises # 53, 54, 55, 63, 66, 68, 74
Clifton
