Question

20. The average annual premium for automobile insurance in the United States is $1503 Insure.com website, March 6, 2014). The following annual premiums (S) are representa- tive of the website's findings for the state of Michigan. 1905 2725 2677 2600 2962 2184 2332 3112 2545 2525 2370 2545 2529 2442 2312 2981 2627 2857 2675 2115
no calculators please! need to know how to work it out the long way, thank you!

Answer 1

a) From the given data,

	Premimum (Xi)	(Xi-Xbar)^2
	1905	417316
	2725	30276
	2677	15876
	2600	2401
	2962	168921
	2184	134689
	2332	47961
	3112	314721
	2545	36
	2525	676
	2370	32761
	2545	36
	2529	484
	2442	11881
	2312	57121
	2981	184900
	2627	5776
	2857	93636
	2675	15376
	2115	190096
Total:	51020	1724940

Sample Mean = 51020/20 = 2551

Sample variance (s²) = 1724940 / (20-1) = 90786.31579

SD (s) = 301.3077

a) The point estiamte of the mean annual automobile insurance premium in Michigan is sample mean = $2551

b)

The 95% confidence interval for the mean annual automobile insurance premium in Michigan is
(xbar - tcrit * s/sqrt(n), xbar + tcrit * s/sqrt(n)) = (2551 - 2.093*301.3077/sqrt(20), 2551 + 2.093*301.3077/sqrt(20)) = (2409.983667,2692.016333)

c)

c) Given The average annula premium for automobile insurance in the US is %1503 is not in the above interval. Thus the annula premium for automobile insurance in the Michigan is not include the nationa average for the US.

The 95% chance that the annula premium for automobile insurance in the US is lies between 2409.983667 and 2692.016333