New Zealand
Level 8 - NCEA Level 3

# Applications of Confidence Intervals

## Interactive practice questions

A clothing store advertises that $65%$65% of its online orders ship within two working days.

A consultancy has been hired to audit a sample of the $10000$10000 orders received over the past month.

a

What sample size would be most appropriate for an audit of the orders delivered over the past month?

$45$45

A

$45000$45000

B

$1$1

C

$5$5

D

$45$45

A

$45000$45000

B

$1$1

C

$5$5

D
b

A random sample of $45$45 of the $10000$10000 orders received over the past month is selected to audit. The audit reveals that $29$29 of these orders were shipped on time.

What is the sample proportion of orders shipped on time? Round your answer to two decimal places.

c

Assuming the advertisement is correct, what is the mean of the distribution that the sample proportion is drawn from?

Round your answer to two decimal places.

d

Assuming the advertisement is correct, what is the standard deviation of the distribution that the sample proportion is drawn from?

Round your answer to four decimal places.

e

Suppose the clothing company does ship $65%$65% of its orders on time. What is probability that the sample proportion in a random sample of $45$45 orders is less than or equal to the sample proportion observed in the audit?

Give your answer as a decimal, rounded to four decimal places.

Easy
Approx 8 minutes
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A recent poll found that of those who have lost weight, $31%$31% believed the most effective strategy involved exercise.

Given this poll, a company that markets exercise equipment is planning to perform a random sample of $300$300 people to inform an advertising strategy.

A batch of $21$21 laptops contains seven that are defective.

A random sample of three laptops is selected.

In a recent census it was found that the proportion of adults that own a car is $\frac{4}{9}$49.

A random sample of $25$25 adults is taken. Let $X$X be the random variable that represents the number of people in the sample that own a car.

### 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