SOCY2339 Assignment 2 Making Inferences About Immigration Attitudes Date Due: October 19th 2018 at 2pm Please submit your assignment with an assignment cover sheet (information on the current version...

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SOCY2339 Assignment 2 Making Inferences About Immigration Attitudes Date Due: October 19th 2018 at 2pm Please submit your assignment with an assignment cover sheet (information on the current version of the cover sheet is available on the Blackboard Announcement page). Assignments should be submitted in the assignment slot at the School of Social Science office on the third floor of the Michie Building (Building 9) Make sure that you: · show a clean copy of working as part marks may be awarded for correct working for any hand calculations · Submit an electronic copy of your log file with your assignment on the online drop box on Blackboard. This is an appendix to your assignment. 1 point will be deducted for any assignment that does not include the log file that has been uploaded. · where possible, your answers should be typed (12 point font). · Answer each question completely. This includes pasting any STATA output into your assignment. Marks:out of 39 + 1 mark for log file (worth 30% of final grade). PART A: Manual Calculations 1. Z scores and the Area under the Normal Curve a. Find the proportion of observations (area under the curve) from a standard normal distribution that satisfies each of the following statements (1.5 marks): i. Z < 1.75="" ii.="" z=""> -0.89 iii. -0.89 <>< 1.75 b. find the value of the standard normal variable z that satisfies each of the following conditions (1 mark): i. the value of z with18% of observations falling below it; ii. the value of z with 74% of observations falling above it. c. suppose respondents were asked about how long they think it takes for an asylum seeker to successfully apply for and receive a visa for living in australia (in months). the variable that represents visa processing time (in months) from the start of their application to receiving their visa has an approximate normal distribution, with a mean of 28 months and a standard deviation of 8 months (3 marks). i. what proportion of asylum seekers would have this process take at least 30 months? ii. what proportion of asylum seekers would have this process take between 9 and 29 months? iii. what is the visa processing time associated with 20% of the asylum seekers falling below it? d. the distribution of foreign born residents with dependent children in australia is skewed to the right, with a µ=3.2 and σ = 1.3. these values of the population are known to you as the researcher who takes a sample of voters from the population of foreign born australian residents in order to estimate mean number of dependent children for each foreign born resident. if you select a random sample of 226 voters: i. describe the sampling distribution of the sample mean. for example, write down the probability distribution and the mean and standard error of this distribution (1.5 marks). ii. find the probability that your sample mean is greater than 4 (1 mark) 2. confidence intervals and hypothesis tests a. a sociologist uses a random sample to survey 508 college students. she finds that the mean amount of confidence in the current immigration minister is 3 (measured on a scale of 1-10 where 1 is the lowest amount of confidence and 10 is the highest amount of confidence). the sample variance (s2) of the variable “confidence in the immigration minister” was 1.5. i. construct a 95% confidence interval for the mean level of confidence in the immigration minister. interpret this interval (2 marks) ii. another sociologist says that he knows that in the population from which this sample is drawn, the mean level of confidence in the immigration minister is actually 5. carry out an appropriate statistical test to examine the null hypothesis. interpret your results (2 marks). b. a random sample of 856 queensland residents were asked what the most important priority is for the australian federal government. “tightening immigration laws” was the first choice for 257 people. i. construct a 95% confidence interval for the proportion of people who picked “tightening immigration laws” as their first choice. interpret this. (2 marks) ii. using the data above, test the null hypothesis that the proportion of people who believe “tightening immigration laws” is the highest priority is 0.16. make sure you use the appropriate estimate of the population proportion (as specified under the null hypothesis) in constructing the standard error. interpret your findings (2marks). 3. confidence intervals, hypothesis tests, and chi square a. a random sample of 67 brisbane adults report that they perceive that the average cost of the getting a visa to live in australia is $1000, with a standard deviation of $125. i. identify and describe the correct probability distribution and explain why this is appropriate (1 mark) ii. construct a 99% confidence interval to estimate the population mean for “perceived immigrant visa cost” in brisbane adults as a whole. fully interpret the interval (2 marks) iii. assume that we know that in the queensland population, the perceived amount of money it costs to get an immigration visa in australia has an average of $1600. is the brisbane sample significantly different from the queensland average? use an alpha of 0.01 (2 marks) b. social science researchers are trying to understand what types of attitudes are related to views about immigration. a random sample of australians was surveyed about a range of attitudes related to immigrants and asylum seekers. below is a contingency table showing the distribution of respondent’s employment status and whether they believe that immigrants are responsible for the amount of crime in australia. do you believe that immigrants are responsible for australia’s crime rate? employed unemployed totals yes 167 67 234 no 85 183 268 totals 252 250 502 i. is there a statistically significant relationship between these variables? you can use the table below for your working. (2 marks) step 1 step 2 step 3 step 4 step5 fo fe fo-fe (fo-fe)^2 (fo-fe)^2/fe ii. compute the column percentages to determine the pattern of the relationship. which group is more likely to think that immigrants are the cause of crime in australia? (2 marks). part b: stata this exercise is to be attempted using the stata software. the data referred to below are stored in the 2016 australian election survey. this is the data file that we have been accessing during tutorial sessions. remember to open a log file at the beginning of your stata session and include an electronic copy of your log file with your assignment. the log file is an appendix, it is not used in lieu of fully answering the questions in your word document (this means you should be including relevenat stata output as part of your answer in the document – not just the log file). 4. use stata to produce frequency tables with and without value labels, for the variable e2_1 measuring whether respondents think providing benefits for migrants has gone too far. what are the value labels corresponding to the lowest and highest scores for this variable? summarize this variable to find the sample mean and standard error (2 marks). 5. use stata to compute a 95% confidence interval for agreement with the statement “all boats carrying asylum seekers should be turned back” (e6_5). interpret this interval. now compute a 99% confidence interval. how has the width of this interval changed and why (2 marks). 6. using stata, test the null hypothesis that australians believe that the amount of immigration allowed in australia should be “reduced a little” (f7). write down the null hypothesis, the test statistic, the p-value and state your conclusion (2 marks). 7. tabulate the variable f8_2 by whether or not the respondent is a member of a trade union (g6). carry out an independent samples t test of f8_2 by g6. state the null hypothesis and determine if the hypothesis can be rejected or not. you can also use the reported ci’s to determine if there is a union membership difference present. interpret the ci’s appropriately (2marks). 8. do a t-test for the mean difference in beliefs about the following two statements; immigrants increase the crime rate (f8_1) and immigrants take jobs away from those who were born in australia (f8_3). interpret your results explaining how you have reached your conclusion.(1 mark) 9. produce a table of opinions on how asylum seekers should be processed (e5) and agreement with the statement “immigrants increase crime” (f8_1). ask stata to also produce a chi square test statistic. report whether these two variables are independent (2 marks) 10. consider all that you have learned about opinions about immigrants and asylum seekers. what do you think are the two take home messages from what you have learned from the stata results above? 2 paragraphs max (3 marks). 1.75="" b.="" find="" the="" value="" of="" the="" standard="" normal="" variable="" z="" that="" satisfies="" each="" of="" the="" following="" conditions="" (1="" mark):="" i.="" the="" value="" of="" z="" with18%="" of="" observations="" falling="" below="" it;="" ii.="" the="" value="" of="" z="" with="" 74%="" of="" observations="" falling="" above="" it.="" c.="" suppose="" respondents="" were="" asked="" about="" how="" long="" they="" think="" it="" takes="" for="" an="" asylum="" seeker="" to="" successfully="" apply="" for="" and="" receive="" a="" visa="" for="" living="" in="" australia="" (in="" months).="" the="" variable="" that="" represents="" visa="" processing="" time="" (in="" months)="" from="" the="" start="" of="" their="" application="" to="" receiving="" their="" visa="" has="" an="" approximate="" normal="" distribution,="" with="" a="" mean="" of="" 28="" months="" and="" a="" standard="" deviation="" of="" 8="" months="" (3="" marks).="" i.="" what="" proportion="" of="" asylum="" seekers="" would="" have="" this="" process="" take="" at="" least="" 30="" months?="" ii.="" what="" proportion="" of="" asylum="" seekers="" would="" have="" this="" process="" take="" between="" 9="" and="" 29="" months?="" iii.="" what="" is="" the="" visa="" processing="" time="" associated="" with="" 20%="" of="" the="" asylum="" seekers="" falling="" below="" it?="" d.="" the="" distribution="" of="" foreign="" born="" residents="" with="" dependent="" children="" in="" australia="" is="" skewed="" to="" the="" right,="" with="" a="" µ="3.2" and="" σ="1.3." these="" values="" of="" the="" population="" are="" known="" to="" you="" as="" the="" researcher="" who="" takes="" a="" sample="" of="" voters="" from="" the="" population="" of="" foreign="" born="" australian="" residents="" in="" order="" to="" estimate="" mean="" number="" of="" dependent="" children="" for="" each="" foreign="" born="" resident.="" if="" you="" select="" a="" random="" sample="" of="" 226="" voters:="" i.="" describe="" the="" sampling="" distribution="" of="" the="" sample="" mean.="" for="" example,="" write="" down="" the="" probability="" distribution="" and="" the="" mean="" and="" standard="" error="" of="" this="" distribution="" (1.5="" marks).="" ii.="" find="" the="" probability="" that="" your="" sample="" mean="" is="" greater="" than="" 4="" (1="" mark)="" 2.="" confidence="" intervals="" and="" hypothesis="" tests="" a.="" a="" sociologist="" uses="" a="" random="" sample="" to="" survey="" 508="" college="" students.="" she="" finds="" that="" the="" mean="" amount="" of="" confidence="" in="" the="" current="" immigration="" minister="" is="" 3="" (measured="" on="" a="" scale="" of="" 1-10="" where="" 1="" is="" the="" lowest="" amount="" of="" confidence="" and="" 10="" is="" the="" highest="" amount="" of="" confidence).="" the="" sample="" variance="" (s2)="" of="" the="" variable="" “confidence="" in="" the="" immigration="" minister”="" was="" 1.5.="" i.="" construct="" a="" 95%="" confidence="" interval="" for="" the="" mean="" level="" of="" confidence="" in="" the="" immigration="" minister.="" interpret="" this="" interval="" (2="" marks)="" ii.="" another="" sociologist="" says="" that="" he="" knows="" that="" in="" the="" population="" from="" which="" this="" sample="" is="" drawn,="" the="" mean="" level="" of="" confidence="" in="" the="" immigration="" minister="" is="" actually="" 5.="" carry="" out="" an="" appropriate="" statistical="" test="" to="" examine="" the="" null="" hypothesis.="" interpret="" your="" results="" (2="" marks).="" b.="" a="" random="" sample="" of="" 856="" queensland="" residents="" were="" asked="" what="" the="" most="" important="" priority="" is="" for="" the="" australian="" federal="" government.="" “tightening="" immigration="" laws”="" was="" the="" first="" choice="" for="" 257="" people.="" i.="" construct="" a="" 95%="" confidence="" interval="" for="" the="" proportion="" of="" people="" who="" picked="" “tightening="" immigration="" laws”="" as="" their="" first="" choice.="" interpret="" this.="" (2="" marks)="" ii.="" using="" the="" data="" above,="" test="" the="" null="" hypothesis="" that="" the="" proportion="" of="" people="" who="" believe="" “tightening="" immigration="" laws”="" is="" the="" highest="" priority="" is="" 0.16.="" make="" sure="" you="" use="" the="" appropriate="" estimate="" of="" the="" population="" proportion="" (as="" specified="" under="" the="" null="" hypothesis)="" in="" constructing="" the="" standard="" error.="" interpret="" your="" findings="" (2marks).="" 3.="" confidence="" intervals,="" hypothesis="" tests,="" and="" chi="" square="" a.="" a="" random="" sample="" of="" 67="" brisbane="" adults="" report="" that="" they="" perceive="" that="" the="" average="" cost="" of="" the="" getting="" a="" visa="" to="" live="" in="" australia="" is="" $1000,="" with="" a="" standard="" deviation="" of="" $125.="" i.="" identify="" and="" describe="" the="" correct="" probability="" distribution="" and="" explain="" why="" this="" is="" appropriate="" (1="" mark)="" ii.="" construct="" a="" 99%="" confidence="" interval="" to="" estimate="" the="" population="" mean="" for="" “perceived="" immigrant="" visa="" cost”="" in="" brisbane="" adults="" as="" a="" whole.="" fully="" interpret="" the="" interval="" (2="" marks)="" iii.="" assume="" that="" we="" know="" that="" in="" the="" queensland="" population,="" the="" perceived="" amount="" of="" money="" it="" costs="" to="" get="" an="" immigration="" visa="" in="" australia="" has="" an="" average="" of="" $1600.="" is="" the="" brisbane="" sample="" significantly="" different="" from="" the="" queensland="" average?="" use="" an="" alpha="" of="" 0.01="" (2="" marks)="" b.="" social="" science="" researchers="" are="" trying="" to="" understand="" what="" types="" of="" attitudes="" are="" related="" to="" views="" about="" immigration.="" a="" random="" sample="" of="" australians="" was="" surveyed="" about="" a="" range="" of="" attitudes="" related="" to="" immigrants="" and="" asylum="" seekers.="" below="" is="" a="" contingency="" table="" showing="" the="" distribution="" of="" respondent’s="" employment="" status="" and="" whether="" they="" believe="" that="" immigrants="" are="" responsible="" for="" the="" amount="" of="" crime="" in="" australia.="" do="" you="" believe="" that="" immigrants="" are="" responsible="" for="" australia’s="" crime="" rate?="" employed="" unemployed="" totals="" yes="" 167="" 67="" 234="" no="" 85="" 183="" 268="" totals="" 252="" 250="" 502="" i.="" is="" there="" a="" statistically="" significant="" relationship="" between="" these="" variables?="" you="" can="" use="" the="" table="" below="" for="" your="" working.="" (2="" marks)="" step="" 1="" step="" 2="" step="" 3="" step="" 4="" step5="" fo="" fe="" fo-fe="" (fo-fe)^2="" (fo-fe)^2/fe="" ii.="" compute="" the="" column="" percentages="" to="" determine="" the="" pattern="" of="" the="" relationship.="" which="" group="" is="" more="" likely="" to="" think="" that="" immigrants="" are="" the="" cause="" of="" crime="" in="" australia?="" (2="" marks).="" part="" b:="" stata="" this="" exercise="" is="" to="" be="" attempted="" using="" the="" stata="" software.="" the="" data="" referred="" to="" below="" are="" stored="" in="" the="" 2016="" australian="" election="" survey.="" this="" is="" the="" data="" file="" that="" we="" have="" been="" accessing="" during="" tutorial="" sessions.="" remember="" to="" open="" a="" log="" file="" at="" the="" beginning="" of="" your="" stata="" session="" and="" include="" an="" electronic="" copy="" of="" your="" log="" file="" with="" your="" assignment.="" the="" log="" file="" is="" an="" appendix,="" it="" is="" not="" used="" in="" lieu="" of="" fully="" answering="" the="" questions="" in="" your="" word="" document="" (this="" means="" you="" should="" be="" including="" relevenat="" stata="" output="" as="" part="" of="" your="" answer="" in="" the="" document="" –="" not="" just="" the="" log="" file).="" 4.="" use="" stata="" to="" produce="" frequency="" tables="" with="" and="" without="" value="" labels,="" for="" the="" variable="" e2_1="" measuring="" whether="" respondents="" think="" providing="" benefits="" for="" migrants="" has="" gone="" too="" far.="" what="" are="" the="" value="" labels="" corresponding="" to="" the="" lowest="" and="" highest="" scores="" for="" this="" variable?="" summarize="" this="" variable="" to="" find="" the="" sample="" mean="" and="" standard="" error="" (2="" marks).="" 5.="" use="" stata="" to="" compute="" a="" 95%="" confidence="" interval="" for="" agreement="" with="" the="" statement="" “all="" boats="" carrying="" asylum="" seekers="" should="" be="" turned="" back”="" (e6_5).="" interpret="" this="" interval.="" now="" compute="" a="" 99%="" confidence="" interval.="" how="" has="" the="" width="" of="" this="" interval="" changed="" and="" why="" (2="" marks).="" 6.="" using="" stata,="" test="" the="" null="" hypothesis="" that="" australians="" believe="" that="" the="" amount="" of="" immigration="" allowed="" in="" australia="" should="" be="" “reduced="" a="" little”="" (f7).="" write="" down="" the="" null="" hypothesis,="" the="" test="" statistic,="" the="" p-value="" and="" state="" your="" conclusion="" (2="" marks).="" 7.="" tabulate="" the="" variable="" f8_2="" by="" whether="" or="" not="" the="" respondent="" is="" a="" member="" of="" a="" trade="" union="" (g6).="" carry="" out="" an="" independent="" samples="" t="" test="" of="" f8_2="" by="" g6.="" state="" the="" null="" hypothesis="" and="" determine="" if="" the="" hypothesis="" can="" be="" rejected="" or="" not.="" you="" can="" also="" use="" the="" reported="" ci’s="" to="" determine="" if="" there="" is="" a="" union="" membership="" difference="" present.="" interpret="" the="" ci’s="" appropriately="" (2marks).="" 8.="" do="" a="" t-test="" for="" the="" mean="" difference="" in="" beliefs="" about="" the="" following="" two="" statements;="" immigrants="" increase="" the="" crime="" rate="" (f8_1)="" and="" immigrants="" take="" jobs="" away="" from="" those="" who="" were="" born="" in="" australia="" (f8_3).="" interpret="" your="" results="" explaining="" how="" you="" have="" reached="" your="" conclusion.(1="" mark)="" 9.="" produce="" a="" table="" of="" opinions="" on="" how="" asylum="" seekers="" should="" be="" processed="" (e5)="" and="" agreement="" with="" the="" statement="" “immigrants="" increase="" crime”="" (f8_1).="" ask="" stata="" to="" also="" produce="" a="" chi="" square="" test="" statistic.="" report="" whether="" these="" two="" variables="" are="" independent="" (2="" marks)="" 10.="" consider="" all="" that="" you="" have="" learned="" about="" opinions="" about="" immigrants="" and="" asylum="" seekers.="" what="" do="" you="" think="" are="" the="" two="" take="" home="" messages="" from="" what="" you="" have="" learned="" from="" the="" stata="" results="" above?="" 2="" paragraphs="" max="" (3="">