Question

A financial planner was interested to know what proportion of people aged 25 – 35 were making regular contributions to an RRSP. A random sample of 330 people in this age group was asked if they are contributing to an RRSP, and only 205 people replied that they were in fact contributing to one. Based on the sample data, construct a 90% confidence interval estimate for the proportion of this age group contributing to an RRSP. Keep 3 decimal places for all calculated values.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 205 / 330 = 0.621

1 - = 1 - 0.621 = 0.379

Z/2 = Z_0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 (((0.621 * 0.379) / 330)

= 0.044

A 90% confidence interval for population proportion p is ,

± E

= 0.621  ± 0.044

= ( 0.577, 0.665 )