Question

The average annual premium for automobile insurance in the United States is $1485. A representative sample of annual premiums for the state of Michigan is contained in the Excel Online file below. Assume the population is approximately normal. Construct a spreadsheet to answer the following questions.

Annual Premium
1931		Sample Size
3150
2376		Point Estimate of Mean (to the whole)
2723
2572		Standard Deviation (4 decimals)
2981
2674		Confidence Coefficient	0.95
2543
2656		Level of Significance
2650
2383		Margin of Error (2 decimals)
2813
2931		C.I. Lower Limit (2 decimals)
2543		C.I. Upper Limit (2 decimals)
2674
2199		National Average for the U.S.	1485
2514
2135		Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the United States?
2325
2409

a. Provide a point estimate of the mean annual automobile insurance premium in Michigan.

$  (to the nearest dollar)

b. Develop a 95% confidence interval for the mean annual automobile insurance premium in Michigan.

($ ,  $ ) (to the nearest cent)

c. Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the United States?

_____Yes or No

What is your interpretation of the relationship between auto insurance premiums in Michigan and the national average?

We would be % confident that auto insurance premiums in Michigan are _______(above or below) the national average.

Answer 1

please atch the data:

1931
3150
2376
2723
2572
2981
2674
2543
2656
2650
2383
2813
2931
2543
2674
2199
2514
2135
2325
2409

point estimate =  x̅ = ΣX/n =    2559

..................

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   19          
't value='   tα/2=   2.0930   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   294.6441   / √   20   =   65.884424
margin of error , E=t*SE =   2.0930   *   65.88442   =   137.897685
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    2559.10   -   137.897685   =   2421.20232
Interval Upper Limit = x̅ + E =    2559.10   -   137.897685   =   2696.99768
95%   confidence interval is (   2421.2   < µ <   2697.0   )

.........

NO, 1485 is not in the interval

.............

We would be 95% % confident that auto insurance premiums in Michigan are _______(above the national average.