Question

4) 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 360 people in this age group was asked if they are contributing to an RRSP, and only 140 people replied that they were in fact contributing to one. Based on the sample data, construct a 94% 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 :

n = 360

x = 140

= x / n =140 / 360 = 0.389

1 - = 1 - 0.389 = 0.611

At 94% confidence level the z is ,

= 1 - 94% = 1 - 0.94 = 0.06

/ 2 = 0.06 / 2 = 0.03

Z/2 = Z0.03 = 1.880

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

= 1.880* (((0.389 * 0.611) / 360)

= 0.048

A 94 % confidence interval for population proportion p is ,

- E < P < + E

0.389 - 0.048< p < 0.389 + 0.048

0.341 < p < 0.437