Topics
9. Sampling and estimation
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AustraliaAU
Year 12

9.03 Approximating the distribution of sample proportions

Lesson
Worksheet
Practice

Interactive practice questions

At a certain university, $15%$15% of students study psychology.

$2000$2000 random students have been asked what subject they are studying. Of those asked, $12%$12% were psychology students.

a

What is the population?

all lecturers at the university

A

the $2000$2000 students asked to rate their lecturers' teaching

B

all students at the university who study psychology

C

all students at the university

D
b

What is the value of the population proportion?

c

What is the value of the sample proportion?

Easy
< 1min

A survey was carried out to investigate the number of teachers in Australian schools who like using the chalkboard to teach. This survey found that in a sample of $1222$1222 teachers, $321$321 liked using the chalkboard, while the rest did not.

Easy
4min

Lachlan wanted to know the proportion of commuters that regularly listen to music on his train. In his carriage, he found that in a sample of $35$35 commuters, $7$7 were listening to music.

Easy
1min

A survey involving $218$218 midwives found that $150$150 of them were aged between $46$46 and $60$60 years.

Easy
1min
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Outcomes

ACMMM174

understand the concept of the sample proportion ˆp as a random variable whose value varies between samples, and the formulas for the mean p and standard deviation √(p(1−p)/n of the sample proportion ˆp

ACMMM175

examine the approximate normality of the distribution of ˆp for large samples

ACMMM176

simulate repeated random sampling, for a variety of values of p and a range of sample sizes, to illustrate the distribution of ˆp and the approximate standard normality of (ˆp−p)/(sqrt(ˆp(1−ˆp)/n) where the closeness of the approximation depends on both n and p

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