代写MATH1041 Statistics for Life and Social Science

MATH1041 Statistics for Life and Social Science

Semester 2, 2016

Assignment

Assignment Release Dates: The assignment requirements will

be released to all students by 9am on the morning of October 4

(Tuesday, Week 10). To allow approximately two weeks for each

student to complete their report, the individual data for your

assignment will be emailed to your ocial university email during

Week 10 as follows. For students with a Monday lab class (not

held in Week 10), before 9am on the morning of Tuesday October

4. For all other students, by 9am on the morning of the day of

the week your lab is held.

Submission date: The start of your lab, week 12. Please submit

to your lab tutor. All pages to be labelled with your student ID.

Students who have a lab on Monday can submit their completed

assignment in their Monday Week 12 lab or Tuesday October 18

(Week 12) to Diana Combe in RC-1032 at her consultation time

代写MATH1041 Statistics for Life and Social Scienceer:

I declare that this assessment item is my own work, except where acknowledged,

and has not been submitted for academic credit elsewhere, and acknowledge that

the assessor of this item may, for the purpose of assessing this item:

Reproduce this assessment item and provide a copy to another member of the

University; and/or,

Communicate a copy of this assessment item to a plagiarism checking service

(which may then retain a copy of the assessment item on its database for the

purpose of future plagiarism checking).

I certify that I have read and understood the University Rules in respect of Student

Academic Misconduct.

Signed: Date:

1

Report Format and Length

You must submit a neatly hand-written or typed report on paper to your lab

tutor

Assignment length: No more than four single-sided A4 pages, including com-

pleted table and gures as attachments plus the above cover sheet (to make ve

pages in total).You are required to include with your submission:

The cover sheet as the rst page.

Your written report (no more than two pages)

The attached table completed with your answers.

Your boxplot and normal probability plot on a single page.

Scenario and Data

In a study of the intelligence levels (measured by IQ, intelligence quotient) of students

enrolled at the world famous Sydney Private University (SPU) its Marketing Department

obtained a simple random sample (SRS) of size n from all full time rst year students

enrolled at SPU in 2016. The selected students were then given a standard IQ test and

their IQ measurements recorded. No other information is available on each student.

Historically the mean IQ of SPU rst year students has been determined to be = 115.

Over 2014-2015 SPU engaged in an aggressive marketing campaign to recruit more intel-

ligent students. The researchers are interested in knowing if this marketing campaign has

had any impact on IQ levels. While the campaign was designed to attract more intelligent

students it is possible it was counterproductive or that other competitor universities had

even better means of attracting higher IQ students in recent years. The researcher wanted

to determine if the true mean IQ in 2016 remains at historical levels or has shifted up or

down. Your job is to analyse the IQ measurements of the SRS provided to you and write

a brief report summarizing your conclusions.

Obtaining the data

The results are available in a le with a name like '3141593.txt', (where 3141593 in the

le name is replaced by your unique student ID number). This le has been sent to you

via email at your ocial university email address.

The le has the IQ recorded for n student responders in separate rows 3 to n + 2.

The rst two rows of the le contain the sample average and sample standard deviation

of these n IQ measurements.

2

Step 1 is to read the data into R or Excel (which ever you choose to work in). You could

get the data into R or Excel and then remove the rst two values (corresponding to the

average and standard deviation) or you could open the le in a text editor and remove

the rst two values prior to getting the data into R or Excel. The data format is simple so

please follow instructions given in the R and Excel How To manuals available on Moodle.

If you experience diculties in entering the data into the computer for analysis please ask

you lab tutor or during the daily consulting hours.

Step 2 is to check that the average and standard deviation of the n IQ results matches

the values given in the rst two rows of the original le sent to you.

Once you have determined that your data has been properly entered and you can repro-

duce the average and standard deviation you are ready to start you analysis.

The Analysis Tasks

The questions you need to answer in your assignment submission are given below.

You will analyse the original data rst followed by an analysis of the data trimmed by

removing outliers as specied in part 3.

You must complete the Table below (page 5) using results from parts 2a and 3 and submit

with your report.

1. Produce a boxplot of your sample of n IQ measurements. Include this boxplot in

your submitted report properly labelled.

Summarize the key features of this boxplot, including central location, spread, ex-

tremes and identify all outliers.

2. (a) Assume now that it is appropriate to use a t distribution for a hypothesis test

and condence interval for the mean .

i. Test the hypothesis that the true mean IQ level of rst year UNSW stu-

dents in 2016 is = 115. You must summarize all steps: The null and

alternative hypotheses relevant to the research objectives stated above, the

value of a suitable test statistic, specication of the appropriate t distri-

bution to be used as a sampling distribution for this statistic, a P-value,

your summary of signicance and conclusion in plain language.

ii. Produce a 95% condence interval for the true mean IQ level of rst year

students enrolled in 2016 at SPU.

Does this condence interval include the historical mean IQ value =

115? Explain whether your condence interval is consistent with your

conclusions from the hypothesis test in part 2(a)ii?

(b) By refering to the boxplot obtained in part 1 brie

y discuss the appropriateness

of the use of the t-distribution as a sampling distribution for the analysis of

parts 2(a)i and 2(a)ii.

3

3. In an attempt to adjust for possible outliers the researcher insisted that you remove

the largest and the smallest IQ measurements from the sample and repeat the

analysis above. This will lead to an analysis based on a trimmed data set with

(n