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Department
Biology
Course
Biology 2244A/B
Professor
Jennifer Waugh
Semester
Fall

Description
Bio statistics 2244A Christina Wang FINAL EXAM REVIEW December 28 , 2011 CHAPTER 6 NOTES CHAPTER 6.1 Major applications of inferential statistics involve the use of sample data o Estimate value of a population parameter o Test some claim (hypothesis) on a population CHAPTER 6.2 REQUIREMENTS FOR USING A NORMAL DISTRIBUTION AS AN APPROXIMATION TO A BINOMIAL DISTRIBUTION: o Sample is a SRS o Conditions for binomial distribution are satisfied Fixed number of trials, independent trials, two categories of outcomes, probabilities remain constant through the trials o Normal distribution can be used approximate the distribution because np 5 and nq 5 Though discussions involve proportions, they can be applied to probabilities or percentages o Percentages must be converted into proportions POINT ESTIMATE: single value used to approximate a population parameter o Sample proportion is the best point estimate of the population proportion Unbiased and the most consistent estimator CONFIDENCE INTERVAL: range of values used to estimate true value of population parameter o Often expressed as probability or area 1 , is the complement of CI o Proportion of times that the confidence interval contains the population parameter Z score is called a critical value, based on: o Sampling distribution of sample proportions can be approximated by a normal distribution o Sample proportions have relatively small chance of falling in the red tails o Denoting the area of each shaded tail by /2, there is a total probability of that is sample proportion will fall in the two red tails 1 Bio statistics 2244A Christina Wang th FINAL EXAM REVIEW December 28 , 2011 o By rule of complements, there is probability of 1 that a sample proportion will faill within the inner region o Z score separating the right tail region is commonly denoted a/2 , referred to as a critical value CRITICAL VALUE: a number of borderline separating sample statistics that are likely to occur from ones that are unlikely to occur/2 , is a critical value it separates the area of /2 in the right tail of the standard normal distribution MARGIN OF ERROR: denoted by E, is max likely difference between observed sample proportion (p-hat) and the true value of population proportion (p) o Found by multiplying critical value and the standard deviation of sample proportions o There is a probability of 1 , or p that a sample proportion will be in error by no more than E, and a probability of that the sample proportion will be in error by more than E ROUND OFF RULE: round CI limits for p to three significant digits CONSTRUCT A CONFIDENCE INTERVAIL FOR P: o Check requirements are satisfied (SRS, conditions for binomial distribution are satisfied, normal distribution can be used to approximate the sample proportions distribution) o Refer to z scores and find critical valuethat corresponds to the confidence level. /2 REMEMBER TO ACCOUNBT FOR ALPHA 2 Bio statistics 2244A Christina Wang th FINAL EXAM REVIEW December 28 , 2011 o Evaluate margin of error o Substitute the calculated and/or given values in a general format for the CI o Round off if necessary Value of E never exceeds 1 REQUIREMENTS FOR ESTIMATING WHEN IS KNOWN: o SRS o Standard deviation of population is known, o Population is normally distributed or n > 30 Sample mean x-bar is the best point estimate of the population mean o Sample mean x-bar tends to be more consistent than other sample statistics o It is an unbiased estimator, because of sample mean center about the population mean o There is a probability of 1 that a sample mean will be in error by no more than E o There is a probability of that the sample mean will be in error by more than E 3
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