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

100	92	121	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	108	100	96	113	88	110
79	115	100	89	114	85	96

(a) Use a calculator to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

x1	=
s1	=
x2	=
s2	=

(b)What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)

Answer 1

(a Using calculator to calculate the given values

= 109.8125

s₁ = 14.896

= 99.143

s₂ = 11.542

(b) Here first we have to find the pooled standard deviation = s_p

s_p = [{(n₁ -1)s₁² + (n₂ -1)s₂²}/(n₁ + n₂ -2)]

= [(15 * 221.8958 + 13 * 133.2088)/(15 + 13)]

s_p = 13.4432

standard error of difference in means = sqrt [s_p2 *(1/n₁ + 1/n₂)]

= sqrt [180.7197 * (1/16 + 1/14)]

= 4.9197

Test statistic = (109.8125 -99.143)/4.9197 = 2.169