Question

An insurance company is interested in estimating the percentage of auto accidents that involve teenage drivers. Suppose the percentage of auto accidents that involved teenage drivers last year was 15%. The company wants to know if the percentage has changed this year. They check the records of 600 accidents selected at random from this year and note that teenagers were at the wheel in 60 of them.

(a) Create a 90% confidence interval for the percentage of all auto accidents that involve teenager drivers this year. Make sure to state any necessary conditions. [3 marks]

(b) Explain what 90% confidence means in this context. [1 mark]

(c) Suppose the insurance company wants to re-estimate the proportion of teenagers who were at the wheel. This time they want the estimate to be correct within 0.02 with 95% confidence. What is the maximum tolerable margin of error proposed by the company? How large a sample would be required? [2 marks]

Answer 1

a. z value for 90% CI is 1.645 as P(-1.645<z<1.645)=0.90

So Margin of Error is

Hence CI is

b. Population percentage of all auto accidents that involve teenager drivers this year will lie in the range of 0.08 to 0.12

c. Here Margin of Error is E=0.02

z value for 95% CI is 1.96 as P(-1.96<z<1.96)=0.95

So