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

4.1

4.7

5.3

3.3

4.8

3.5

2.4

3.1

3.5

5.2

2.8

Assume that the crime rate distribution is approximately normal in both regions. Use a calculator to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

x1	=
s1	=
x2	=
s2	=

What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ₁ − μ₂. Do not use rounded values. Round your answer to three decimal places.)

(b) Find a 98% confidence interval for

μ₁ − μ₂.

(Round your answers to two decimal places.)

lower limit
upper limit

Answer 1

a)

x1 =3.55

s1 =0.83

x2 =3.87

s2 =0.95

std error =√(S21/n1+S22/n2)=	0.380
test stat t =(x1-x2-Δo)/Se =	-0.832

b)

Point estimate of differnce =x1-x2     =	-0.317
for 98 % CI & 9 df value of t=		2.821
margin of error E=t*std error                   =	1.073
lower bound=mean difference-E     =	-1.39
Upper bound=mean differnce +E      =	0.76