STA60001-Statistical Practice
Question 1
In October 2010, Galaxy Research was commissioned by Australian Marriage Equality and Parents and Friends of Lesbians and Gays to conduct a study of opinions of Australians with regard to same sex marriage. Interviews were conducted using CATI (computer assisted telephone interviewing) with telephone numbers randomly selected from electronic White Pages. In a sample of 1050 respondents, 651 Australians agreed that same-sex couples should be able to marry.
a) Construct (show all calculations) and interpret a two-sided 95% WALD confidence interval for the population proportion of Australians in October 2010 who agree that same-sex couples should be able to marry?
b) Is the following statement true or false? Explain in detail why the statement is true or false. The confidence interval constructed in part a) represents the interval within which 95% of sample proportions would fall within, if we were to take repeated samples of size 1050 from the population.
c) What statistical symbol is used to represent the proportion of all Australians who agree that same-sex couples should be able to marry? Is this a parameter or a statistic?
d) A similar study was conducted in May 2009 and 60% of Australians agreed that same-sex couples should be allowed to marry. Conduct a hypothesis test and write a report to decide if the 2010 study is evidence that the proportion of Australians who agree with same sex marriage has significantly increased from the 60% established in 2009. (Use α = .05). Data can be found in the file same_sex_marry.sav
Question 2
Probabilities to be written correct to 3 decimal places or correct to 1 decimal place if written as percentages. Please paste in appropriately sized screenshots of the probability calculator when used to respond to any of the following questions. There are no formal reports or 8 steps required for this question. They are all short answer questions.
After years of teaching driver education, an instructor knows that students hit an average of µ = 10.5 orange cones while driving the obstacle-course in their final exam. The distribution of run-over cones is approximately normal with a standard deviation of σ = 4.8
a) If we randomly select a student from the population of students in driver education class
(i) What is the probability that they will hit more than 15 cones?
(ii) What is the minimum number of cones that a student could hit that would put them in the top 20% in the distribution of cones hit?
b) A new driving instructor is employed who has implemented a new driver instructor program. To determine if the new program has been effective, he randomly selects 16 students from the current driver instructor program and finds that the mean number of orange cones hit by the 16 students is 9.2. Assume that the population standard deviation of cones hit remains 4.8 for the following questions in part b.
For each question please provide justification by using an appropriate distribution and illustrating how you reached your conclusion.
(i) Is this evidence that the new program has been effective in improving the performance of the students in lowering the number of cones hit from the previous education program?
(ii) What is the maximum mean number of orange cones that could have been hit by the 16 students to conclude that the new program has been effective in improving the performance of the students in lowering the number of cones hit from the previous education program?
(iii) The new instructor was not sure whether the new program would have improved or not the performance of the students in terms of the number of cones hit. What values of the mean number of cones for a sample of 16 students would lead the instructor to conclude that the program had significantly changed the mean number of cones that the students hit?
c) The new driving instructor makes further changes in their second year at the school and takes a random sample of 25 students in the second year and finds that the average number of cones that these students run over is now 8.5 cones and the standard deviation of the number of cones that the 25 students run over is 3.8 cones. The new driving instructor does not want to make any assumptions about the current population standard deviation. Determine if there is evidence that the new program has changed the performance of students in comparison to the initial old program? Construct manually an appropriate 95% confidence interval to respond to this question, showing all calculations and justify your response.
d) Complete the following statement: In the older program where the distribution of number of cones run over by students is normally distributed with mean of 10.5 cones and standard deviation of σ = 4.8, then we can say that 95% of students would run over between ___ and ____ number of cones.
e) Explain the difference between standard deviation and standard error. In order to describe the differences, use the scenario presented in this question. Specifically refer to the example presented here about students hitting cones.
Question 3
Lead is an environmental pollutant especially worthy of attention because of its damaging effects on the neurological and intellectual development of children. In the eighties researchers collected data on lead absorption by children whose parents worked at a factory in Oklahoma where lead was used in the manufacture of batteries. The concern was that children might be exposed to lead inadvertently brought home on the bodies or clothing of their parents. Levels of lead (in micrograms per decilitre (mcg/dl)) were measured in blood samples taken from 33 children who might have been exposed in this way. They constitute the Exposed group.
The researchers formed a Control group by making matched pairs. For each of the 33 children in the Exposed group they selected a matching child of the same age, living in the same neighbourhood, and with parents employed at a place where lead is not used. The lead measurements are shown in Table 1 and you will need to create the SPSS datafile. The means and standard deviations are given in Table 2 so that you can check your data entry.
a) The researchers hypothesised that the lead levels of the children exposed are significantly higher those in the control group.
i. Check the assumptions of the hypothesis test you would choose to respond to the researcher’s question. Comment on each assumption and paste in all necessary graphs and or tables to support your comments.
ii. Regardless of the conclusion reached in ai), conduct the hypothesis test and write a report summarizing your findings (Use α = .05). Remember to follow the report format as covered in the notes.
b) For non-pregnant adults, a level of lead below 25 mcg/dL is considered to be acceptable. The researchers hypothesised that the lead levels of the children exposed are significantly different from 25 mcg/dL
i. Check the assumptions of the hypothesis test you would choose to respond to the researcher’s question. Comment on each assumption and paste in all necessary graphs and or tables to support your comments.
ii. Regardless of the conclusion reached in bi), conduct the hypothesis test and write a report summarizing your findings (Use α = .05). Remember to follow the report format as covered in the text.
