Question

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.

(Round your answers to two decimal places.)

lower limit
upper limit

Answer 1

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