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10. Samples and estimation
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AustraliaVIC
VCE 12 Methods 2023

10.03 Approximate the distribution

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

U34.AoS4.7

the definition of sample proportion as a random variable and key features of the distribution of sample proportions

U34.AoS4.4

statistical inference, including definition and distribution of sample proportions, simulations and confidence intervals: - distinction between a population parameter and a sample statistic and the use of the sample statistic to estimate the population parameter - simulation of random sampling, for a variety of values of 𝑝 and a range of sample sizes, to illustrate the distribution of 𝑃^ and variations in confidence intervals between samples - concept of the sample proportion as a random variable whose value varies between samples, where 𝑋 is a binomial random variable which is associated with the number of items that have a particular characteristic and 𝑛 is the sample size - approximate normality of the distribution of P^ for large samples and, for such a situation, the mean 𝑝 (the population proportion) and standard deviation - determination and interpretation of, from a large sample, an approximate confidence interval for a population proportion where 𝑧 is the appropriate quantile for the standard normal distribution, in particular the 95% confidence interval as an example of such an interval where 𝑧 ≈ 1.96 (the term standard error may be used but is not required).

U34.AoS4.12

simulate repeated random sampling and interpret the results, for a variety of population proportions and a range of sample sizes, to illustrate the distribution of sample proportions and variations in confidence intervals

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