Question

A random sample of n₁ = 10 regions in New England gave the following violent crime rates (per million population).

x₁: New England Crime Rate

3.5

3.9

4.0

4.1

3.3

4.1

1.8

4.8

2.9

3.1

Another random sample of n₂ = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population).

x₂: Rocky Mountain Crime Rate

3.7

4.3

4.5

5.3

3.3

4.8

3.5

2.4

3.1

3.5

5.2

2.8

x1	= 3.55
s1	= .83
x2	= 3.87
s2	= .94

Find a 98% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

Lower Limit

Upper Limit

Answer 1

	Values ( X )	Σ ( Xi- X̅ )2	Values ( Y )	Σ ( Yi- Y̅ )2
	3.5	0.0025	3.7	0.0289
	3.9	0.1225	4.3	0.1849
	4	0.2025	4.5	0.3969
	4.1	0.3025	5.3	2.0449
	3.3	0.0625	3.3	0.3249
	4.1	0.3025	4.8	0.8649
	1.8	3.0625	3.5	0.1369
	4.8	1.5625	2.4	2.1609
	2.9	0.4225	3.1	0.5929
	3.1	0.2025	3.5	0.1369
			5.2	1.7689
			2.8	1.1449
Total	35.5	6.245	46.4	9.7868

Mean X̅ = Σ Xi / n
X̅ = 35.5 / 10 = 3.55
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 6.245 / 10 -1 ) = 0.83

Mean Y̅ = ΣYi / n
Y̅ = 46.4 / 12 = 3.87
Sample Standard deviation S_Y = √ ( (Yi - Y̅ )² / n - 1 )
S_Y = √ ( 9.7868 / 12 -1) = 0.94

Confidence interval :-

Critical value t(α/2, DF) = t(0.02 /2, 19 ) = 2.5395 ( From t table )

DF = 19

Lower Limit =
Lower Limit = -1.28
Upper Limit =
Upper Limit = 0.64

98% Confidence interval is ( -1.28 , 0.64 )