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10.03 Approximating the distribution of sample proportions

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

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

To practice her archery, Sandy marked a small interval on the board with length $5$5 centimetres. Sandy takes $240$240 shots at the board from a certain distance, with $151$151 landing between the small interval.

Easy
1min
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Outcomes

4.5.2.2

consider the approximate normality of the distribution of 𝑝̂ for large samples

4.5.2.3

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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