Question

Automobile mechanics conduct diagnostic tests on 150 new cars of particular make and model to determine the extent to which they are affected by a recent recall due to faulty catalytic converters. They find that 42 of the new cars tested do have faulty catalytic converters. What is the point estimate for the population proportion for a​ 99% confidence interval based on these sample​ results?

Answer 1

Solution :

Given that,

n = 150

x = 42

= x / n = 42/150 = 0.28

point estimate = 0.28

1 - = 1 - 0.28 = 0.72

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576* (((0.28 * 0.72) / 150) = 0.0944

A 99 % confidence interval for population proportion p is ,

- E < P < + E

0.28 - 0.0944 < p < 0.28+ 0.0944

0.1856< p < 0.3744

The 99% confidence interval for the population proportion p is : (0.1856 ,0.3744)