Question

A car manufacturer wants to estimate the proportion of cars of a certain model that have crashed. If we want a confidence level of 99% that the sample proportion is in error by no more than 4%, how many cars must be sampled? A random sample of 600 families in Smogsville indicated that 120 of them owned an iPhone. Find a 95% confidence interval for the true proportion of all families living in Smogsville who own an iPhone.

Answer 1

To estimate the proportion of cars that have crashed, a car manufacturer needs to sample at least 672 cars with a 99% confidence level and a 4% error margin.

Step-by-step explanation:

To estimate the proportion of cars of a certain model that have crashed with a 99% confidence level and an error margin of 4%, we can use the formula for sample size:

n = (Z^2 * p * (1-p)) / (E^2)

Where:

• n = sample size
• Z = Z-value for the desired confidence level (2.58 for 99% confidence level)
• p = estimated proportion (0.5, assuming an equal chance of crashing)
• E = maximum error margin (0.04)

By plugging in the values, we can solve for n:

n = (2.58^2 * 0.5 * 0.5) / (0.04^2) = 671.06

Rounding up to the nearest whole number, we need to sample at least 672 cars.