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