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# PSY 315 Week 5 û Chapter problems

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Date Created: 11/13/15

Week 5 Page 1 Week 5 Chapter problems PSY315 Katherine Sainz University of Phoenix Week 5 P a g e 2 Individual AssignmentWeek 5 Chapter 7 14 Evolutionary theories often emphasize that humans have adapted to their physical environment One such theory hypothesizes that people should spontaneously follow a 24 hour cycle of sleeping and waking even if they are not eXposed to the usual pattern of sunlight To test this notion eight paid volunteers were placed individually in a room in which there was no light from the outside and no clocks or other indications of time They could turn the lights on and off as they wished After a month in the room each individual tended to develop a steady cycle Their cycles at the end of the study were as follows 25 27 25 23 24 25 26 and 25 Using the 5 level of significance what should we conclude about the theory that 24 hours is the natural cycle That is does the average cycle length under these conditions differ significantly from 24 hours a Use the steps of hypothesis testing b Sketch the distributions involved c EXplain your answer to someone who has never taken a course in statistics Research Hypothesis The average cycle length will differ significantly from 24 hours Null Hypothesis The average cycle length will not differ from 24 hours Population 1 People of the general population Population 2 People within the testing rooms A N8 25225232425225 M 25 hours dfiN 1K 1 m24hiuur5 55 25 252 as 2 25 25 as as as 24 25 253 25 El 25 25 441 1 1n Week 5 Page l3 3 55 III S EF1n43 53 5E 1quot43 Ina N a quot39 511 a 13m at Two tailad t cutoff for Elf Iquot at 5 aigt canBa 2365 tIaI I25 aa aM 142 233 Since the t statistic is greater than the critical value we reject null hypothesis We can conclude that natural cycle isn39t 24 hours tdjguibmumwi ldf3 I I I I I I I I I I5 T 3 1 2 3 at t aaaaa r Una tailadtaat TEWUtEi39EthEt m H m in 4 Ltd IL39I Shaded araa ELEIEEIEI Week 5 Page4 C From the known significance level we can find that the critical value which outlines the minimum difference between the mean and hypothesized value to make it statistically significant We notice our findings of our t score which is greater than critical t This small difference is statically important in making natural cycle different from 24 hours Chapter 8 A Use the steps of hypothesis testing The two tailed statistics for the above observations Null Hypothesis H0 1 uz 0 vs Hg 1 uz 0 Formula for test statistics z 1fz39 u f1f2l T E 2 39 Kl x a1 32 Using above two tailed statistics Rejection region can be defined as Z lt quotZoe2 01 Z gt Zen2 Critical Value Here significance level is 005 So 20025 196 The sample is selected independently and randomly from the population The population size is sufficiently large in both samples Calculation Calculating test statistics for both samples Week 5 Page 5 38 35 2 32 52 V20 30 Calculating p value 2648 Pzlt 2648 00109 with z 2648 and DF2030 248 Conclusion Because the calculated test statistics is equal to 2648 which is less than critical value of 196 We can reject the null hypothesis because there is enough evidence at 5 level of significance that there is a difference in the mean number of test in experimental group and control group B sketch the distributions involved tdj5tr j1riunw 1df43 I I I I I I I I I 43 I39 5 4 3 2 1 1 39n J 1 f IDWIEIalEIlilIIEIdl fault 5quot 39II39IIIIIIJLEII iIIIeIdl fast 32h adle dl area 10500 C EXplain your answer to someone who is familiar with the t test for a single sample but not with the t test for independent means Week 5 Page 6 The t test for independent means is extension of the one sample t test where the variability of the two independent sample means is taken into account to check the validity of information where the estimation the standard error of the mean difference based on experimental and control group sample variances and their sizes is checked Chapter 9 17 Do students at various colleges differ in how sociable they are Twenty five students were randomly selected from each of three colleges in a particular region and were asked to report on the amount of time they spent socializing each day with other students The results for college X was a mean of 5 hours and an estimated population variance of 2 hours for College Y M 4 S2 15 and for College Z M 6 S2 25 What should you conclude Use the 05 level a Use the steps of hypothesis testing b figure the effect size for the study and c eXplain your answers to a and b to someone who has never had a course in statistics A Research Hypothesis Groups of students are not sociable Null Hypothesis All groups of students are sociable Groups Count S am Average Variance X 25 125 5 2 Y 25 100 4 15 Z 25 150 6 25 Cutoff for t 2 72 at 005 two tailed Below 72 on the graph 270 cutoff equals 313 kg EMZ GMJE5 5E4 53 5E12m2 3 1 H 2 E E 5E 1125 25 EE21535 3 3 Week 5 Page7 s2 25 F 1a5 s2 2 Because the calculated F statistics is equal to 125 which is greater than 31239 we reject the null hypothesis meaning the groups of students are significantly different socially B RE 53TH 2 mm 26 L SEMI 3 SEEM 3532U3 C This test we had to figure out if the groups of students were different socially In the information provided we know that the means of the groups are different Some school has better socializing ratio than other schools and 2577 of variation in the amount of time they spent socializing each day with other students is eXplained by selection of the different schools Chapter 11 11 Make up a scatter diagram with 10 dots for each of the following situations a perfect positive linear correlation b large but not perfect positive linear correlation c small positive linear correlation d large but not perfect negative linear correlation e no correlation f clear curvilinear correlation A Perfect positive linear correlation Week 5 Page 8 12 1E 1E 12 B Large but not perfect positive linear correlation Week 5 Page 9 12 1U l 2 5t E 1E 12 C Small positive linear correlation 12 1E 15 D Not perfect negative linear correlation Week 5 Page 10 12 10 12 E No correlation 12 1U 1E 12 Week 5 Page 11 12 For problems 12 to 14 do the following a Make a scatter diagram of the scores b describe in words the general pattern of correlation if any c figure the correlation coefficient d figure whether the correlation is statistically significant use the 05 significance level two tailed e explain the logic of what you have done writing as if you are speaking to someone who has never heard of correlation but who does understand the mean deviation scores and hypothesis testing and f give three logically possible directions of causality indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved and why Four research participants take a test of manual dexterity high scores mean better dexterity and an anxiety test high scores mean more anxiety The scores are as follows Person Dexterity Anxiety 1 1 10 2 1 8 3 2 4 4 4 2 A Chart Title 12 1D Q 8 Q E I QSeHesl 391 2 Q D J 15 1 15 2 25 a1 55 atteringr Week 5 Page 12 B The plot above shows a strong negative correlation and is either linear or curvilinear As anxiety levels increase so dexterity decreases C Dexterity 1 1 E 1 ME 2 4 Anxiety 1 n43 Eil M 4 4 Z Elli quot Michquot Ma 2 We use the t test and insert the values of r and the sample size df n 2 4 2 2 at 05 E We must find the correlation using the correlation coefficient Co efficient of determination R2 0979962 096 Therefor 96 percent of the variation in dexterity level is accounted by anxiety level Also there is positive association between the anxiety level and the dexterity level F directions of causality can be lower anxiety level causing higher dexterity higher dexterity causing lower anxiety or high levels of a 3 factor causing both higher and lower anxiety and dexterity

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