1. Many times in statistical analysis, we do not know the TRUE mean of a population of interest. This is why we use sampling to be able to generalize the results of a sample to the entire population. One way that we can estimate the TRUE mean based upon a single sample is through a CONFIDENCE INTERVAL. Criteria for Creating a Confidence Interval 1)Sample must be a SRS (Simple Random Sample) 2)CLT (Central Limit Theorem) MUST apply 3)Each subject in the sample must be independent  Most Important

2. The idea of a confidence interval is that based upon the statistic (a mean or proportion) of the sample and a determined confidence level, a range of numbers is established that is believed to enclose the TRUE mean of the population from which the sample originated. Sample mean TRUE mean will fall somewhere within this interval

3. To find this interval, we need to know the z-score above and below the middle that will enclose the desired confidence level (%). We can get this from the z-score table and our knowledge of the bell curve. The z-score that cuts off the desired confidence level is called a critical value (z*) Look up the lower tail’s % on the table for the z-score This is the critical value for an 80% confidence level

4. What would be the critical values for the following common confidence levels? Draw a bell curve to help with finding the percentages needed. 90% 95% 99%

5. What would be the critical values for the following common confidence levels? Draw a bell curve to help with finding the percentages needed. 90% ………………………………………………………… 95%........................................................... 99% …………………………………………………………. 1.645 1.96 2.575

6. Once you have the critical value, you can calculate the interval by using the following formula. Confidence Interval = statistic ± z* ∙ standard error For estimating the population MEAN, the formula would be… This is under the assumption that we know the standard deviation of the population (  )

7. Example: A simple random sample of 50 Big City University freshmen are collected and given an IQ test. The mean of the sample is 112 and the standard deviation of the population of IQ scores is 15. Create a 95% confidence interval for the TRUE mean IQ score of the population of all Big City freshmen. (107.84, 116.16)

8. Confidence Intervals with Proportions

10. Steps for Confidence Intervals 1)Make sure the distribution is normally distributed (ie: CLT applies) a) Means: n ≥ 30 or population is normal b) Proportions: np ≥ 10 AND n(1-p) ≥ 10 2)Use the confidence interval formula to plug in the values based upon the desired confidence level. CI = statistic ± z* ∙ standard error

11. Confidence Interval Practice 1)(9.18, 10.82) 2)(0.32, 0.48 ) 3)(48.04, 51.96) 4)CLT does not apply 5)(61.84, 76.16) 6)(0.37, 0.43)