Populations and Samples

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

The approximate normal distribution of the sample proportions

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.

a

Calculate the sample proportion of $\hat{p}$^`p`, of those teachers surveyed who like using the chalkboard.

Write your answer correct to $3$3 decimal places.

b

Using your answer from part (a), estimate the standard deviation, $\hat{\sigma}$^`σ`, of the random variable $\hat{P}$^`P`, for such samples of size $1222$1222.

Round your answer to $3$3 decimal places.

Easy

Approx 4 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