Question

According to the Australian Bureau of Statistics the estimated proportion of people aged 18-25 resident in NSW at 30 June 2017, who identified as female was 0.490142.

The number of students identifying as female aged 18-25 enrolled in 2018 Autumn Statistical Design and Analysis (SDA) as at 30 Mar 2018 was 304 and the remainder was 240.

Provide the proportion of the 2018 Autumn SDA enrolment who identified as females aged 18-25, using correct notation

What statistical test would we perform to determine if there is difference in the proportion of students identifying as female18-25 enrolled in SDA compared to the proportion of people identifying as female resident in NSW in June 2017? (1 mark)

What condition needs to be met for us to perform this test and is it met? (1 mark)

Answer 1

• The number of female with age 18-25 in Autumn SDA = 304, total number of 18-25 aged people are = 304+240 = 544

So, the proportion = = 304/544 = 55.88% = 0.5588

• We should conduct the usual large sample test of proportion for a single sample which is based on Central Limit theorem, and the test statistic is a z-statistic.
• The condition that needs to be satisfied is , here n = 544, , so we have

  

So, the condition is satisfied