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Biology

Biology 2244A/B

Jennifer Waugh

Fall

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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
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