Populations and Samples

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

Confidence Intervals

A sample of size $170$170 is taken from the population, and the sample proportion is found to be $0.55$0.55.

Standard Normal Probability | z-value |
---|---|

$0.9$0.9 | $1.282$1.282 |

$0.925$0.925 | $1.440$1.440 |

$0.95$0.95 | $1.645$1.645 |

$0.975$0.975 | $1.960$1.960 |

$0.99$0.99 | $2.326$2.326 |

$0.995$0.995 | $2.576$2.576 |

a

State the $z$`z`-value that corresponds to a $90%$90% confidence interval.

b

Use the table of values to calculate the $90%$90% confidence interval for the true proportion.

Express your answer in the form $\left(\editable{},\editable{}\right)$(,), and give your answer to two decimal places.

c

Which of the following statements about the confidence interval are correct? Select all that apply.

There is a $90%$90% probability that the true proportion lies between $0.49$0.49 and $0.61$0.61.

A

The probability that the true proportion lies within $\left(0.49,0.61\right)$(0.49,0.61) is $0$0 or $1$1.

B

We have $90%$90% confidence that the true proportion lies between $0.49$0.49 and $0.61$0.61.

C

The true proportion lies between $0.49$0.49 and $0.61$0.61.

D

There is a $90%$90% probability that the true proportion lies between $0.49$0.49 and $0.61$0.61.

A

The probability that the true proportion lies within $\left(0.49,0.61\right)$(0.49,0.61) is $0$0 or $1$1.

B

We have $90%$90% confidence that the true proportion lies between $0.49$0.49 and $0.61$0.61.

C

The true proportion lies between $0.49$0.49 and $0.61$0.61.

D

Easy

Approx 8 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