It is reported that COVID19 vaccine hesitancy across Australia has fallen to 16.7% on the 12th September 2021. Suppose there is a claim that in NSW, vaccine hesitancy is higher than the one reported for across Australia.

A random sample 440 NSW adult residents was collected and 77 of them expressed COVID-19 vaccine hesitancy.

Use this sample to calculate the 95% confidence interval of the proportion of all NSW adult residents who are hesitant toward COVID-19 vaccine and interpret it

You should show all steps required (4 marks) and write the interpretation(1 marks).