A random sample of "1= 10 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 98 107 111 116 151 134 126 96 122 111 121 133 142 123 95 91 A random sample of "2= 14 regions in western Kansas gave the following information for people over 50 years old.

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A random sample of "1 10 communities in western Kansas gave the following information for people under 25 years of age.
%3D
X1: Rate of hay fever per 1000 population for people under 25
98 107 111 116 151 134 126 96 122 111 121 133 142 123 95 91
A random sample of "2 regions in western Kansas gave the following information for people over 50 years old.
12: Rate of hay fever per 1000 population for people over 50
81 112 103 102 78 76 112 113 104 119 92 106 97 106
Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group
over 50 has a lower rate of hay fever? Use a = 0.05 State the null and alternate hypotheses.
Question 6 options:
O Ho P1>H2, H1 H1=#2:
C Ho P1<H2;H 1:1>H2:
(Ctrl)
Transcribed Image Text:A random sample of "1 10 communities in western Kansas gave the following information for people under 25 years of age. %3D X1: Rate of hay fever per 1000 population for people under 25 98 107 111 116 151 134 126 96 122 111 121 133 142 123 95 91 A random sample of "2 regions in western Kansas gave the following information for people over 50 years old. 12: Rate of hay fever per 1000 population for people over 50 81 112 103 102 78 76 112 113 104 119 92 106 97 106 Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use a = 0.05 State the null and alternate hypotheses. Question 6 options: O Ho P1>H2, H1 H1=#2: C Ho P1<H2;H 1:1>H2: (Ctrl)
Expert Solution
Step 1

Given Information:

Under 25 years of age:

Sample size n1=16

Sample mean x¯1=98+107+111+....9116=117.3125

Standard deviation s1=98-117.31252+107-117.31252+........91-117.3125216-1=17.54506

Over 50 years of age:

Sample size n2=14

Sample mean x¯2=81+112+103+....10614=100.07143

Standard deviation s2=81-100.071432+112-100.071432+........106-100.07143214-1=13.62387

Significance level α=0.05

 

State the hypothesis as follows:

Let μ1 denote the population mean of hay fever for age group under 25 years of age and μ2 denote the population mean of hay fever for age group over 50 years of age.

Null Hypothesis H0:μ1=μ2 

Alternative Hypothesis H1:μ1>μ2 i.e., age group over 50 has a lower rate of hay fever than age group under 25 years age. In other words, age group under 25 years of age has a higher rate of hay fever than age group over 50 years age. 

 

 

 

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