Question 3(13 points)

You are the marketing manager for an online retail store. Currently, for every 1000 people that visit your website you make 250 sales. You have decided to trial a new website design on 100 visitors to the website to see if the sales rate improves.

1. [2 marks] How should the 100 people be selected? Explain why this is important.

1. [3 marks] Assuming that the new website design has had no effect, what distribution best describes the number of sales out of 100? Give all relevant parameters of this distribution.

1. [3 marks] Would it be reasonable to approximate the distribution in (b) with a Normal distribution? If so, what would you use for the mean and standard deviation?

1. [3 marks] The trial runs and of the 100 people shown the new website 28 make purchases. If the underlying rate of sales hadn't actually changed (i.e. the new website had no effect) how likely is it to get 28 or more sales out of 100 visits? Show a z-score as part of your working.

1. [2 marks] Assuming that there would be some costs involved with swapping to the new design, do you think it would be worthwhile for the store to change its website? [Note, the value you calculated in part (d) is known as ap-value, it should be useful in guiding your decision].