A random sample of n_{1} = 16 communities in western Kansas gave the following information for people under 25 years of age.
x_{1}: 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 n_{2} = 14 regions in western Kansas gave the following information for people over 50 years old.
x_{2}: 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 x_{1}, s_{1}, x_{2}, and s_{2}. (Round your answers to two decimal places.)
x_{1} | = |
s_{1} | = |
x_{2} | = |
s_{2} | = |
What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ_{1} − μ_{2}. Do not use rounded values. Round your answer to three decimal places.)
(b) Find a 90% confidence interval for
μ_{1} − μ_{2}.
(Round your answers to two decimal places.)
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 |
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