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

96	88	122	130	90	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

93	110	103	99	113	88	110
79	115	100	89	114	85	96

x1

= 109.38

s1

= 15.84

x2

= 99.86

s2

= 11.84

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.)

Answer 1

	people under 25 ( X )	Σ ( Xi- X̅ )2	people over 50 ( Y )	Σ ( Yi- Y̅ )2
	96	179.0244	93	43.1649
	88	457.1044	110	108.7849
	122	159.2644	103	11.7649
	130	425.1844	99	0.3249
	90	375.5844	113	180.3649
	123	185.5044	88	133.8649
	112	6.8644	110	108.7849
	93	268.3044	79	423.1249
	125	243.9844	115	238.0849
	95	206.7844	100	0.1849
	125	243.9844	89	111.7249
	117	58.0644	114	208.2249
	97	153.2644	85	212.2849
	122	159.2644	96	12.7449
	127	310.4644
	88	457.1044
Total	1750	3889.7504	1394	1793.4286

Mean X̅ = Σ Xi / n
X̅ = 1750 / 16 = 109.38
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 3889.7504 / 16 -1 ) = 16.1

Mean Y̅ = ΣYi / n
Y̅ = 1394 / 14 = 99.57
Sample Standard deviation S_Y = √ ( (Yi - Y̅ )² / n - 1 )
S_Y = √ ( 1793.4286 / 14 -1) = 11.75

x1

= 109.38

s1

= 16.10

x2

= 99.57

s2

= 11.75

Test Statistic :-

t = 1.922