Question

# A random sample of n1 = 16 communities in western Kansas gave the following information for...

A random sample of n1 = 16 communities in western Kansas gave the following information for people under 25 years of age.

x1: Rate of hay fever per 1000 population for people under 25

 98 92 120 126 94 123 112 93 125 95 125 117 97 122 127 88

A random sample of n2 = 14 regions in western Kansas gave the following information for people over 50 years old.

x2: Rate of hay fever per 1000 population for people over 50

 95 112 103 98 111 88 110 79 115 100 89 114 85 96

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 90% confidence interval for

μ1 − μ2.

 lower limit upper limit

from given data:

x1 =109.63

s1 =14.94

x2 =99.64

s2 =11.67

 std error =√(S21/n1+S22/n2)= 4.866 test stat t =(x1-x2-Δo)/Se = 2.051

b)

 Point estimate of differnce =x1-x2     = 9.982 for 90 % CI & 13 df value of t= 1.771 margin of error E=t*std error                   = 8.618 lower bound=mean difference-E     = 1.36 Upper bound=mean differnce +E      = 18.60