Question

Financial investment ~ Kevin is looking to invest his money in a local investment company called Robin Hood financial services. To ensure his investment is safe and has good returns, he randomly surveys people who invested with the company and asks whether they would recommend the company for investment. Of the 420 people surveyed, 265 recommend Robin Hood financial services for investment.

Using this data, Kevin wants to estimate the actual proportion of people who recommend Robin Hood financial services for investment.

What is the lower AND upper bound for a 90% confidence interval? Give your answer to 4 decimal places.

Answer 1

Solution :

n = 420

x = 265

= x / n = 265 / 420 = 0.631

1 - = 1 - 0.631 = 0.369

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (((0.631 * 0.369) / 420)

= 0.039

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.631 - 0.039 < p < 0.631 + 0.039

0.592 < p < 0.700