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Homework Packet Three_S2022 PSYCHOLOGY B5 HOMEWORK PACKET THREE (20PTS) 1. What are the assumptions / conditions of a z-test 2. How is variance determined when conducting a z-test? 3. How is error determined when conducting a z-test? What is error for a z-test called? 4. What is the formula for z-obt? 5. A researcher predicts that a particular treatment will lower scores. If this researcher uses a one-tailed test, will the critical region be to the right or left of the mean in the distribution? Draw and label the distribution, indicating which tail the researcher should find his z-obtained if his treatment does lower scores significantly. 6. Explain the following (in complete sentences): a. When it is appropriate to use a one-tailed test. b. When it is appropriate to use a two-tailed test. | H o m e w o r k P a c k e t T h r e e - R i e s s 1 Name: 7. A researcher wants to see if viewing a documentary on systemic racism will significantly change people’s understanding of systemic racism. The researcher randomly select 36 people, shows them the documentary, and give them a questionnaire that is intended to measure understanding of systemic racism. The mean score on the questionnaire for this sample of people is x = 73.0. Historically, the average score for the population (who had not seen the film) has been 68 (µ = 68.0), with a standard deviation of σx = 12.0 (assume the alpha level = .05). Follow the six of the eight steps of hypothesis testing to test the effect of the movie on viewer’s understanding. Step I. Research question: II. Statistical test: III. Hypotheses: (Statement): (Statistical): (Statement): (Statistical): IV. Alpha and Critical Value: Number of tails? Alpha: α: Critical Value: : H0 : H0 : Ha : zcrit : Ha | H o m e w o r k P a c k e t T h r e e - R i e s s 2 V. Obtained value: VI. Make a decision: μ: : σx 8. You hypothesize that children will be more relaxed when they are tested with their mothers present. On a standard test, the national average relaxation score of children tested without their mothers present is 44.26 (σx =5.86). You test the relaxation of children when their mothers are present. Follow the six of the eight steps of hypothesis testing to test the effect of having mothers present effects children’s scores. 50 53 63 30 64 60 41 40 ΣX = n = 35 25 44 41 44 46 64 58 X = Step I. Research question: II. Statistical test: III. Hypotheses: (Statement): (Statistical): : Ha : Ha | H o m e w o r k P a c k e t T h r e e - R i e s s 3 (Statement): (Statistical): IV. Alpha and Critical Value: Number of tails? Alpha: α: Critical Value: V. Obtained value: VI. Make a decision: : zcrit μ: : σx : H0 : H0 | H o m e w o r k P a c k e t T h r e e - R i e s s 4 9. Under what circumstances is a t–test statistic used instead of a z-test for a hypothesis test? 10. What are the degrees of freedom (df)? 11. Provide the appropriate names, symbols, and formulas for each of the following statistical steps, in t-tests. Variance Error Obtained Name: Name: Name: 12. Students taking a statistics course at Bakersfield College reported studying more hours per test than did Bakersfield College students in general (X = 6.0 hours per test); s2x= 2.75, t (14) = 3.00, p < .05. a. how many participants were in this study? b. what is the obtained value? c. calculate the 95% confidence interval. | h o m e w o r k p a c k e t t h r e e - r i e s s 5 c. using symbols, write the statistical null and alternative hypotheses. d. determine the critical region using a one-tailed test with alpha = .05. e. conduct the statistical test to test your hypothesis (estimated population variance is given (this time), calculate estimated standard error of the mean and t-obtained). f. make a decision. | h o m e w o r k p a c k e t t h r e e - r i e s s 6 13. daniel wants to know whether a commonly prescribed drug does improve the attention span of 1st grade students with attention deficit disorder (add). he knows that the mean attention span for students with add who are not taking the drug is 1.36 (population) minutes long. his sample of 12 students taking the drug yielded a mean of 2.36. justin can find no information regarding σx , so he calculated s2x =1.86. a. identify the independent and dependent variables. b. in a sentence, state the null hypothesis being tested. 14. on a standardized spatial skills task, the population mean is 14.35 (µ = 14.35) correct solutions. a psychologist tests 7 individuals who have brain injuries in the right cerebral hemisphere. use the following data, determine whether right-hemisphere damage results in significantly reduced performance on the spatial skills task. the scores are as follows: 11, 13, 12, 8, 12, 16, 14 conduct a hypothesis test. step i. research question: ii. statistical test: iii. iv. alpha and critical value: number of tails? alpha: α: df: (statement): : h0 (statistical): : h0 hypotheses: (statement): : ha (statistical): : ha critical value: : tcrit | h o m e w o r k p a c k e t t h r e e - r i e s s 7 v. obtained value: μ: estimated population variance estimated standard error t-obtained vi. make a decision: | h o m e w o r k p a c k e t t h r e e - r i e s s 8 15. select one of the following population means. collect sample data from the other students, siblings, cousins, neighbors, etc. to compare to the population means. your “n” must be at least 12. complete 7 steps to test your hypothesis. hours per week spent studying: µ = 5.0 hours per week socializing (pre-covid): µ = 8.0 hours per week exercising (pre-covid): µ = 4.0 hours per day grooming (pre-covid): µ = .80 number of days, out of the last seven had enough sleep to feel rested (pre-covid): µ = 3.93 number of times, in the last two weeks, had 5 or more drinks in a single setting (pre-covid): µ = 2.19 number of doughnuts consumed per month: µ = 2.58 | h o m e w o r k p a c k e t t h r e e - r i e s s 9 .05.="" a.="" how="" many="" participants="" were="" in="" this="" study?="" b.="" what="" is="" the="" obtained="" value?="" c.="" calculate="" the="" 95%="" confidence="" interval.="" |="" h="" o="" m="" e="" w="" o="" r="" k="" p="" a="" c="" k="" e="" t="" t="" h="" r="" e="" e="" -="" r="" i="" e="" s="" s="" 5="" c.="" using="" symbols,="" write="" the="" statistical="" null="" and="" alternative="" hypotheses.="" d.="" determine="" the="" critical="" region="" using="" a="" one-tailed="" test="" with="" alpha=".05." e.="" conduct="" the="" statistical="" test="" to="" test="" your="" hypothesis="" (estimated="" population="" variance="" is="" given="" (this="" time),="" calculate="" estimated="" standard="" error="" of="" the="" mean="" and="" t-obtained).="" f.="" make="" a="" decision.="" |="" h="" o="" m="" e="" w="" o="" r="" k="" p="" a="" c="" k="" e="" t="" t="" h="" r="" e="" e="" -="" r="" i="" e="" s="" s="" 6="" 13.="" daniel="" wants="" to="" know="" whether="" a="" commonly="" prescribed="" drug="" does="" improve="" the="" attention="" span="" of="" 1st="" grade="" students="" with="" attention="" deficit="" disorder="" (add).="" he="" knows="" that="" the="" mean="" attention="" span="" for="" students="" with="" add="" who="" are="" not="" taking="" the="" drug="" is="" 1.36="" (population)="" minutes="" long.="" his="" sample="" of="" 12="" students="" taking="" the="" drug="" yielded="" a="" mean="" of="" 2.36.="" justin="" can="" find="" no="" information="" regarding="" σx="" ,="" so="" he="" calculated="" s2x="1.86." a.="" identify="" the="" independent="" and="" dependent="" variables.="" b.="" in="" a="" sentence,="" state="" the="" null="" hypothesis="" being="" tested.="" 14.="" on="" a="" standardized="" spatial="" skills="" task,="" the="" population="" mean="" is="" 14.35="" (µ="14.35)" correct="" solutions.="" a="" psychologist="" tests="" 7="" individuals="" who="" have="" brain="" injuries="" in="" the="" right="" cerebral="" hemisphere.="" use="" the="" following="" data,="" determine="" whether="" right-hemisphere="" damage="" results="" in="" significantly="" reduced="" performance="" on="" the="" spatial="" skills="" task.="" the="" scores="" are="" as="" follows:="" 11,="" 13,="" 12,="" 8,="" 12,="" 16,="" 14="" conduct="" a="" hypothesis="" test.="" step="" i.="" research="" question:="" ii.="" statistical="" test:="" iii.="" iv.="" alpha="" and="" critical="" value:="" number="" of="" tails?="" alpha:="" α:="" df:="" (statement):="" :="" h0="" (statistical):="" :="" h0="" hypotheses:="" (statement):="" :="" ha="" (statistical):="" :="" ha="" critical="" value:="" :="" tcrit="" |="" h="" o="" m="" e="" w="" o="" r="" k="" p="" a="" c="" k="" e="" t="" t="" h="" r="" e="" e="" -="" r="" i="" e="" s="" s="" 7="" v.="" obtained="" value:="" μ:="" estimated="" population="" variance="" estimated="" standard="" error="" t-obtained="" vi.="" make="" a="" decision:="" |="" h="" o="" m="" e="" w="" o="" r="" k="" p="" a="" c="" k="" e="" t="" t="" h="" r="" e="" e="" -="" r="" i="" e="" s="" s="" 8="" 15.="" select="" one="" of="" the="" following="" population="" means.="" collect="" sample="" data="" from="" the="" other="" students,="" siblings,="" cousins,="" neighbors,="" etc.="" to="" compare="" to="" the="" population="" means.="" your="" “n”="" must="" be="" at="" least="" 12.="" complete="" 7="" steps="" to="" test="" your="" hypothesis.="" hours="" per="" week="" spent="" studying:="" µ="5.0" hours="" per="" week="" socializing="" (pre-covid):="" µ="8.0" hours="" per="" week="" exercising="" (pre-covid):="" µ="4.0" hours="" per="" day="" grooming="" (pre-covid):="" µ=".80" number="" of="" days,="" out="" of="" the="" last="" seven="" had="" enough="" sleep="" to="" feel="" rested="" (pre-covid):="" µ="3.93" number="" of="" times,="" in="" the="" last="" two="" weeks,="" had="" 5="" or="" more="" drinks="" in="" a="" single="" setting="" (pre-covid):="" µ="2.19" number="" of="" doughnuts="" consumed="" per="" month:="" µ="2.58" |="" h="" o="" m="" e="" w="" o="" r="" k="" p="" a="" c="" k="" e="" t="" t="" h="" r="" e="" e="" -="" r="" i="" e="" s="" s="">