Question

Ignacio is curious about the average age of cars in the commuter lot at Mis large university. He takes a random
sample of 16 cars and finds that their average age is 2 = 14.5 years and their standard deviation is 8, = 4.6
years. The distribution of ages in the sample was roughly symmetric with no obvious outliers.
Based on this sample, which of the following is a 90% confidence interval for the mean age of cars (in years) in
this commuter lot?

Answer 1

Answer:

Between 12.614 years and 16.386 years

Step-by-step explanation:

Given that:

Mean age (μ) = 14.5 years, standard deviation (σ) = 4.6 years, number o sample (n) and the confidence interval (c) = 90% = 0,9

α = 1 -c = 1 -0.9 = 0.1

$\frac{\alpha }{2} = \frac{0.1}{2} = 0.05$

The z score of $\alpha /2$ is the same as the z score of 0.45 (0.5 - 0.05). This can be gotten from the probability distribution table. Therefore:

$z_{0.05}=1.64$

The margin of error (e) = $z_{0.05}\frac{\sigma}{\sqrt{n} }$ = $1.64*\frac{4.6}{\sqrt{16} }=1.886$

The interval = μ ± e = 14.5 ± 1.886 = (12.614 ,16.386)

Answer 2

Answer:

12.48, 16.52

Step-by-step explanation:

Took it on Khan