Populations and Samples

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

Applications of Confidence Intervals

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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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