Populations and Samples

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Estimating population size from sample

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 $AB$`A``B`.

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

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Make inferences from surveys and experiments: A determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem B using methods such as resampling or randomisation to assess

Use statistical methods to make a formal inference