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# Psychological Research II PSYC 202

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This 10 page Class Notes was uploaded by Ozella Cassin on Monday October 19, 2015. The Class Notes belongs to PSYC 202 at Radford University taught by Pamela Jackson in Fall. Since its upload, it has received 12 views. For similar materials see /class/224716/psyc-202-radford-university in Psychlogy at Radford University.

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Date Created: 10/19/15

Inferences about the Mean of a Single Population STAT Chap 8 METH Chap 13 The Standard Normal Curve Remember the standard normal curve 7 5 a theoretwcal samphng dwstrbutwon of mdeual 5c re 7 5 created by a mathemaucal equauon r computes the probabmues that an eventwm occur under specmed con moms 7 has had all of us scores convened to Z scores to standardwze n We used it to determine probabilities and percentile ranks of individual scores sampled a population when the mean and standard deviation of the population was known Percent areas from the mean 0 to specified zscores in the standard normal curve Sampling Distributions A sarnbiing distributan ufa nurnber ufscures frum tne pupulatiun We can then calculate tne Mr W standard deuiation i or thuse scores tneir uariabii ty abuut tne rn ean Sampling Distribution of the Mean if we re interested in drawing a sample or subieots frum tne pupulatiun and making an inference i based un gruup data then we nee a sarn biing distribution ufthe rnean 5o we d draw an in nite nurnber sarn l Remember the Central Limit em The Central Limit Theorem states that the sampling distribution of the mean will approximate ge rvel the sample size N is lar enoug 7 Even ittne underi ing distribution of population data l5 not normally distri uteo In addition it states that the mean ofthe sampling distribution will equal the p ofthe population and the variance will egual that ofthe population divided by the N 0 subjects in each sample Because ofthis we can test hypotheses about means So We tested hypotheses sort of about a single score drawn 39om a population z scores In order to test hypotheses about grou s of ubjects drawn 39om a population we basically use the Central Limit Theorem to obtain the sampling distribution of the mean when the null hypothesis is true One big difference is that we calculate the standard error of the mean instead of using the standard deviation Why Because as can be seen below the variability in a distribution ofmeans is smaller than that in a distribution of raw scores Standard Error of the Mean un unnuml t quotum mm or IM m unmiaul nu MinH m mt simult ul aim mm 0 Keep in mind a s standard deviation tor sample data a U standard deviation tor population data Hypothesis testing with one sample of data Data collected by the state highway patrol over an extended period indicated that the average speed on a stretch of interstate was 72 mph with o 15 They instituted a new procedure aimed at reducing the speed closer to 65 mph they had more officers patrol during peak travel hours The data was collected for 3 weeks and the 50 observations obtained revealed an average of 68 mph with 5 12 Was their manipulation successful Review Hypothesis testing steps 1 Choose the appropriate test statistical model 2 Create the Null and Alternative Hypotheses 3 State the criteria for rejecting Null 4 Do the calculations 5 Make the decision Reject Null or Not 6 Draw Conclusions 7 Write the results up in an APAstyle format Steps 1 2 amp 3 constitute Setting up the Hypothesis Test Choose the appropriate test The data are continuous interval or ratiotype data miles per hour We want to know whether there is a difference between a sample mean and the population mean So we only measured 1 sample of data If one knows the mean and standard deviation of the population one uses the standard normal curve to test the hypothesis a ztest Set up the Hypothesis test H0 Y p a 05 H1 7 u twotailed 0 Now we need the rejection region or critical values for making our decision 0 With ztests you always use the standard normal curve values If a 05 and it is a nondirectional twotailed test then we now t a we will reject the null if the 2 value is in the outer 025 of the curve half of 05 HE xquot p a 05 H1 x1e p twotailed 2mm 1196 Now we do the calculations Calculations z 68 a 72 L 15 L 350 7 0711 i 1 8856 2 1213 Decisi o n ch ical 1195 Zubtained 39189 Decision 189 lt 196 therefore do not reject the HD Conclusion quotaquot r 44 difference in the average mph on that stretch of road Write the results in APA style The state highway patrol were not able to signi cantly reduce the average speed on a particular stretch ofhighway by increasing the mbe ofpatrol cars in a 3 week period Before the increase in of cers e average speed was 72 mph and a erwards it was 68 mph This data t L m was not signi cant zN50 188 pgt 05 Confidence Interval for the ztest Confidence Intervai c1 c195 Y 2 we in Harmereimerzw 1 as Whatifi wanted a 99 CV Then a 01 therefure 2M 2 SE Exampie preerds speedrng probiem C195SEJ19621213 6841577 Cunfdence intervai 72 1577 e 53 8423 What dues rt mean7 The t distribution The tdistribution is used if the population standard deviation is not known estimate the standard deviation of tne popuiation usingthe sarnpie standard deviation The Irdistr bution m but rs siightiy drrrerent The t distribution The exact shape Because the curve l5 different riding 0 sample SlZeS i 3 df Nil where N 1 Sample Size Surveys ofhow much the students liked the food served in a college cafeteria had been collected over several years at a large universi T were 3 responses on a 7point scalet at w summed to yield a total ranging 39om 3 to 21 The satis ction score avera e 61 for the last 3 years The company in char e ofthe cafeteria changed during the summer he new cafeteria manager wanted a quick test of how the new of 30 students using the same questions scale The sample returned an average score of 188 with a standard deviation of47 lsthe new company an improvement over the old company Review Hypothesis testing Choose the appropriate test statistical model Create the Null and Alternative Hypotheses State the criteria for rejecting Null Do the calculations Make the decision Reject Null or Not Draw Conclusions Write the results up in an APAstyle format NOFJ19gt N9 Steps 1 2 amp 3 constitute Setting up the Hypothesis Test Set up the Hypothesis test H0 7 p a 05 H1 Y u twotailed 0 Now we need the rejection region or critical values for making our decision 0 With ttests you use the Critical values of 139 table in the appendix Hypothesis test a05 H0 X p H u twotailed dfN 1 30 1 29 tcritical 2 39 045 Calculations I quot 39illl ilfNei r 18 8 7161 2 7 H H 30 5 4772 t u 31465 8581 Decision tcritical 12045 39 tubtaineo 315 Decision 315gt2o45 therefore rejectthe HD Conclusion The cafeteria is doing a signi cantly better job in terms of student satisfaction Write the results in APA style 0 The average satisfaction score forth cafeteria food across se eral yea rs has been 151 on a scale ranging from 3 to 21 The satisfaction score increased to 188 wi c m an e sample t test was used to analyze the difference between the old and the new an e n w company scored significantly higher t29 315 p lt 05

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