Question

# A random sample of n1 = 10 regions in New England gave the following violent crime...

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 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.

 lower limit upper limit

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