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日期：2018-10-18 09:43

STAT5002 Introduction to Statistics – Semester 1, 2018

Assignment

Due: Thu 7/6/2018 1pm

Submit via Turnitin on canvas

Notes and Instructions:

This assignment is assessed. It carries a weight of 8% towards your final mark for

STAT5002.

You may discuss the questions with others but you must submit your own individual

reports with your own working and words.

Presentation of your assignment is marked.

Show all R code or calculation used to answer the questions in your report.

Do NOT include your name in the assignment.

Problem 1 A researcher has conducted an experiment to compare the growth of tomato seedlings

using a newly derived compost and the industry standard commercial compost. The

result of the experiment is included in compost.csv. What is your conclusion from the

experiment?

The answer to this should not be more than one page.

Problem 2 A politician has contacted you with the following email.

I think policy X is an effective measure to curb illegal immigration. The poll

results indicated that 55% of the 200 people randomly surveyed agree with

me. A statistician told me that the p-value is large so there isn’t evidence that

majority agree with me. I didn’t understand it so the statistician gave me a

confidence interval instead. The number doesn’t make sense to me since there

are more than 50% of the people agree with me! To be precise 55%! Can

you recalculate this p-value and confidence interval for me and also could you

explain it in simpler terms to me so I can understand it?

The answer to this should not be more than one page.

Problem 3 Criminologists are interested in the effect of demographic characteristics and police expenditure

on crime rates. This has been studied using aggregate data on 47 states of the

USA for 1960 contained in the file uscrime.txt. The data set contains the columns as

described in Table 1.

(a) The sample correlation between crime rate and police expenditure in 1959 suggests

that an increase to police expenditure in 1959 increases the crime rate. Explain.

crime = read.table("uscrime.txt", header=T)

cor(crime$Crime, crime$Po2)

## [1] 0.6667141

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(b) In the previous question, we saw that the sample correlation between crime rate in

1960 and police expenditure in 1959 was positive. The model fitted below suggests

however that an increase in police expenditure in 1959 decreases the crime rate in

1960. Explain.

coef(lm(Crime ~ Po1 + Po2, data=crime))

## (Intercept) Po1 Po2

## 158.2646 256.1526 -178.2880

(c) Fit the most appropriate model for the given data. Show all your codes to get your

final model.

The answer to Problem 3 should not be more than three pages.

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Variable Description

M percentage of males aged 14–24 in total state population

So indicator variable for a southern state

Ed mean years of schooling of the population aged 25 years or over

Po1 per capita expenditure on police protection in 1960

Po2 per capita expenditure on police protection in 1959

LF labour force participation rate of civilian urban males in the age-group 14–24

M.F number of males per 100 females

Pop state population in 1960 in hundred thousands

NW percentage of nonwhites in the population

U1 unemployment rate of urban males 14–24

U2 unemployment rate of urban males 35–39

Wealth wealth: median value of transferable assets or family income

Ineq income inequality: percentage of families earning below half the median income

Prob probability of imprisonment: ratio of number of commitments to number of offenses

Time average time in months served by offenders in state prisons before their first release

Crime crime rate: number of offenses per 100,000 population in 1960

Table 1: List of variables in uscrime.txt