Question

The following values are annual car insurance premiums ($) from a 2014 sample of car owners living in Michigan. Use it to answer/do the following. 1905 2725 2677 2600 2962 2184 2332 3112 2545 2525

(a) Estimate the average car insurance premium.

(b) Develop a 90% confidence interval for the mean in (a)

(c) Develop a 95% confidence interval for the mean in (a).

(d) Develop a 99% confidence interval for the mean in (a).

(e) The national average car premium was $1,503 in 2014. Compare this to your answers for (b)-(d). What can you say about car insurance in Michigan?

Answer 1

(a) Average = (1905 + 2725 + 2677 + 2600 + 2962 + 2184 + 2332 + 3112 + 2545 + 2525) / 10 = 2556.7

The sample standard deviation is calculated as 354.74

____________________________________________

(b) 90% CI, = 0.10, and the t critical for df = n - 1 = 9 is 1.833

The Confidence Interval is given by , where

Therefore the 90% CI is 2556.7 205.62

_________________________________________________

(c) 95% CI, = 0.05, and the t critical for df = n - 1 = 9 is 2.262

The Confidence Interval is given by , where

Therefore the 95% CI is 2556.7 253.75

__________________________________________________

(d) 99% CI, = 0.01, and the t critical for df = n - 1 = 9 is 3.25

The Confidence Interval is given by , where

Therefore the 99% CI is 2556.7 364.58

___________________________________________________

(e) The average car insurance in Michigan is greater than the national average of $1503, as none of the above confidene intervals contains the value of $1503.

_____________________________________________________