Lecture 9 Outline of Last Lecture I Z Score Example Questions Psych 311 1st Edition Outline of Current Lecture I Review II Probability and Proportions III Random Sampling IV Probability and the Normal Distribution V Determining Probabilities of Obtaining Specific Scores X VI Final Note VII Other Variations Current Lecture I Review Inferential Stats statistical technique that allows us to study samples and make generalizations about the population they are drawn from whatever is true about the sample is true about the poulation sampling error discrepency between sample and population that is always present by understanding probabilities we can understand how to interpret the affect of sampling error on that process II Probability and Proportsions Probability in a situation in which servral outcomes are possible the probability for any particular outcome is a fraction or proportion of the total number of possible outcomes the likelihood that something will happen Proportion the physical area a specific section of the whole Probabilities are expressed in terms of fractions Proportions expressed in terms of decimals 0 00 1 00 range of possible outcomes Can be used interchangeably if expressed in terms of percentages 0 100 either none or all IV Random Sampling Random sampling unbiased sampling select X s randomly These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Must meet two requirements every individual has equal chance of being selected probabilities stay constant from one selection to the next to insure this you must do sampling with replacement Sampling with replacement select sample study then replace before choosing new sample sampling same X twice is possible problem is that it duplicates that individuals data this wouldn t be representative we don t meet the requirements in psychological studies because we don t put back used samples V Probability and the Normal Distribution Normal Distribution symmetrical greatest frequency in middle lowest frequencies on ends mean median mode has a SD of 1 00 has very specific proportions or area associated with it within 1SD 68 26 of data 2SD 95 44 of data 3SD 99 98 In standardized distributions probability defined as proportion of area under curve Standardized distribution has a mean of 0 00 and a SD of 1 00 Z Scores allow us to easily devide up the distribution tail of distribution is the smaller side under the curve from X body of distribution is the larger side from X under the curve V Determining Probabilities of Obtaining Specific Scores X Step 1 sketch distribution identify mean and SD locate X Step 2 Shade portion of distribution you re concerned with Step 3 Estimate proportion in shaded area Step 4 Convert X value into Z score value Step 5 Consult Unit Normal Table to arrive at proportions negative sign doesn t matter in table but must remember to input negative sign later Step 6 Identify whether concerned with body or tail of distribution Step 7 Estimate proportion from Step 4 VI Final Note Can NEVER has proportion greater than 1 00 or a negative proportion If either of the above occur you ve messed up VII Other Variations Finding proportions probabilities associated with Z score Finding proportion probabilities associated with X Finding Z or X from probabilities proportions Can go from X Z P or P Z X using Unit normal table Z Score formula and conversions from Z Score to X