A household survey in 2017 recorded information on 152 people who were retired from the Australian...

A household survey in 2017 recorded information on 152 people who were retired from the Australian labour force. Of these, 105 reported government pension or allowance as their main source of income. Calculate a 95% confidence interval to estimate the proportion of all Australian retirees who have government pension or allowance as the main source of income. Give your answers to 3dp:

The lower limit is

The upper limit is

Solutions

Expert Solution

Solution :

Given that,

n = 152

x = 105

Point estimate = sample proportion = = x / n = 105/152=0.691

1 - = 1- 0.691 =0.309

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z/2 * $\sqrt$ ((( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((0.691*0.309) / 152)

E = 0.073

A 95% confidence interval is ,

- E < p < + E

0.691-0.073 < p < 0.691+0.073

(0.618,0.764)

orchestra answered 1 year ago

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