NZ Level 7 (NZC) Level 2 (NCEA) Estimating population size from sample

## Interactive practice questions

The heights (in cm) of a population of 3 people are $A$A, $B$B and $C$C.

a

List all possible samples of size 2 without replacement. For example if the first 2 are selected we can write that as $AB$AB.

Use commas to separate different samples.

b

If $A=171$A=171, $B=153$B=153 and $C=162$C=162, complete the following table:

Sample Values (cm) Sample Mean
$171$171, $153$153 $\editable{}$ cm
$171$171, $162$162 $\editable{}$ cm
$153$153, $162$162 $\editable{}$ cm
c

What is the mean of the distribution of all possible sample means?

d

What is the population mean?

e

Is the mean of the sample means equal to the population mean?

Yes

A

No

B

Yes

A

No

B
Easy
Approx 5 minutes

The heights (in cm) of a population of 3 people are $A$A, $B$B and $C$C.

The weights (in kg) of a population of 5 people are F, G, H, I and J.

The weights (in kg) of a population of 5 people are $F$F, $G$G, $H$H, $I$I and $J$J.

### Outcomes

#### S7-2

S7-2 Make inferences from surveys and experiments: A making informal predictions, interpolations, and extrapolations B using sample statistics to make point estimates of population parameters C recognising the effect of sample size on the variability of an estimate

#### 91264

Use statistical methods to make an inference