a) Suppose that the weekly rental house in ($) in a particular western suburb in Sydney follow a normal distribution and we want to estimate the mean rental price of all houses in this particular suburb.

A sample of 20 weekly house rentals was collected and it was found to have a sample mean of $539 and sample standard deviation of $ 69.426

Calculate the 95% confidence interval to estimate the mean of all rental houses in this particular suburb in Sydney.

b) In2014 the climate Institute reported that 70% of people in Australia believed that climate change was largely due to human activity.

A recent survey of 1480 people in Sydney, 1096 indicated they believed that climate change was largely due to human activity.

Carry out an appropriate hypothesis test to determine whether the proportion of people in Sydney is different from the national proportion (70%) with respect to this issue. Use=0.05

Show all workings step by step