SECTION 7.2 Estimating a Population Proportion

Practice  Pg  #6-8 (Finding Critical Values)  #9-11 (Expressing/Interpreting CI)  #17-20 (Finding Margin of Error)

Answers: Pg  #5-8 (Finding Critical Values)   #9-11 (Expressing/Interpreting CI)  / /  /  #17-20 (Finding Margin of Error)  

Topic 3 – Critical Example  Finding z α /2 for a 95% Confidence Level 1. Find  /2 2. Subtract the result from Find the corresponding z score.

Topic 3 – Check Yo Self! Confidence Level  Critical Value, z  /2 90% % %

Topic 4 – Margin of Error Definition  Margin of Error: When data from a simple random sample are used to estimate a population proportion p, the margin of error, denoted by E, is the maximum likely difference (with probability 1 – , such as 0.95) between the observed proportion and the true value of the population proportion p.

Topic 4 – Margin of Error Formula Important Notes Margin of Error for Proportions

Topic 4 – Check Your Self Assume that a sample is used to estimate a population proportion p. Find the margin of error, E, that corresponds to the given statistics and confidence level. Round the margin of error to three decimal places. a) 90% confidence, sample size is 500, 20% are successes. b) 99% confidence, sample size is 300, 25% are successes.

Topic 2 – Expressing A Confidence Interval 3 different ways to write a confidence interval

Topic 2 – Check Yo Self Assume that a sample is used to estimate a population proportion p. Find the margin of error, E, that corresponds to the given statistics and confidence level. Round the margin of error to three decimal places. a) 90% confidence, sample size is 500, 20% are successes. b) 99% confidence, sample size is 300, 25% are successes. ***Now express your answers from before as an interval.

Topic 2 – Putting it All Together How To Guide: Constructing a Confidence Interval 1. Verify the sample is a simple, random sample and that the conditions for a binomial distribution are met. 2. Find the critical value z α /2 3. Evaluate the margin of error. 4. Find the values of the confidence interval limits. 5. Round the resulting confidence interval limits to three decimal places.

Topic 2 – Example Constructing a Confidence Interval: Poll Results A poll of 1501 randomly selected U.S adults showed that 70% of the respondents believe in global warming. 1. Find the margin of error that corresponds to a 95% confidence interval. 2. Find the 95 th confidence interval estimate of the population proportion p. 3. Based on the results, can we safely conclude that the majority of adults believe in global warming?

Topic 3 – Determining Sample Size Objective  Determine how large the sample should be in order to estimate the population proportion p. Requirements  The sample must be a simple random sample of independent subjects.  When an estimate of is known:  When an estimate of is unknown:

Topic 3 – Determining Sample Size Important Note Round-off Rule for Determining Sample Size If the computed sample size n is not a whole number, round the value of n up to the next larger whole number.

Topic 3 – Determining Sample Size Example How Many Adults Use the Internet?  An executive for E-Bay wants to determine the current percentage of U.S adults who now use the Internet. How many adults must be surveyed in order to be 95% confident that the sample percentage is in error by no more than three percentage points?  Use this result from a Pew Research Center poll: In 2006, 73% of U.S adults used the Internet.  Assume that we have no prior information suggesting a possible value of the proportion.

Topic 3 – Point Estimate and E Finding the Point Estimate and E from a Confidence Interval

Topic 3 – Point Estimate and E Example The article “High-Dose Nicotine Patch Therapy,” by Dale Hurt includes the statement: “Of the 71 subjects, 70% were abstinent from smoking at 8 weeks (95% confidence interval, 58% to 81%).” Use that statement to find the point estimate and margin of error E.

Practice  Pg  #5-8 (Finding Critical Values)  #9-11 (Expressing/Interpreting CI)  #17-20 (Finding Margin of Error)  #21-24 (Constructing Confidence Intervals)  #25-28 (Determining Sample Size)  #31, 32 (Application Problems)

Answers: Pg  #5-8 (Finding Critical Values)   #9-11 (Expressing/Interpreting CI)  / /  /  #17-20 (Finding Margin of Error)  

Answers: Pg  #21-24 (Constructing Confidence Intervals)  < p < < p <  < p < < p <  #25-28 (Determining Sample Size)  , ,  #31, 32 (Application Problems)  31. a.) b.) < p<0.514 c.) no, proportion can easily be 0.5  32. a.) b.) < p < c.) Yes, p will be larger than 0.5