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

## Interactive practice questions

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

A sample of size $130$130 is taken from the population, and the sample proportion is found to be $0.69$0.69.

A sample of size $140$140 is taken from the population, and the sample proportion is found to be $0.53$0.53.

A sample of size $180$180 is taken from the population, and the sample proportion is found to be $0.63$0.63.

### Outcomes

#### S8-2

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

#### 91582

Use statistical methods to make a formal inference