MATLAB: An Introduction with Applications
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Author: Amos Gilat
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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 | 129 | 93 | 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 | 108 | 103 | 98 | 112 | 88 | 110 |
| 79 | 115 | 100 | 89 | 114 | 85 | 96 |
(i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to four decimal places.)
| x1 | = |
| s1 | = |
| x2 | = |
| s2 | = |
What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.)
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 | 129 | 93 | 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 | 108 | 103 | 98 | 112 | 88 | 110 |
| 79 | 115 | 100 | 89 | 114 | 85 | 96 |
(c) Find (or estimate) the P-value.
P-value > 0.250
0.125 < P-value < 0.250
0.050 < P-value < 0.125
0.025 <P-value < 0.050
0.005 < P-value < 0.025
P-value < 0.005
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant
.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(e) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.
Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.
Fail to reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.
Fail to reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.
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