The following values are annual car insurance premiums ($) from a 2014 sample of

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

2370 2545 2529 2442 2312 2981 2627 2857 2675 2115

a) Estimate the average car insurance premium.

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

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

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

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?

Explanation / Answer

a) average car insurance premium =2551.00

b)here degree of freedom df=n-1=19

for 90% CI, and for 19 df t=1.729

hence confidence interval =mean +/- t*std error =2434.501 ; 3072.001

c)for 95% CI, t=2.093

confidence interval = 2409.984 ; 3181.644

d)

for 99% CI, t=2.093

confidence interval = 2358.246 ; 3413.022

from above it seems that Michigan interval is greater then national average car premium hence it is greater

X 1905.000 2725.000 2677.000 2600.000 2962.000 2184.000 2332.000 3112.000 2545.000 2525.000 2370.000 2545.000 2529.000 2442.000 2312.000 2981.000 2627.000 2857.000 2675.000 2115.000 mean(X) 2551.000 std deviation(S) 301.308 std error =S/(n)1/2 67.374

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