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 92 119 127 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 94 109 100 97 111 88 110 79 115 100 89 114 85 96 (i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) 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 α = 0.05. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A random sample of n1 = 16 communities in western Kansas gave the following information for people under 25 years of age.
| 100 | 92 | 119 | 127 | 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.
| 94 | 109 | 100 | 97 | 111 | 88 | 110 |
| 79 | 115 | 100 | 89 | 114 | 85 | 96 |
| x1 | = |
| s1 | = |
| x2 | = |
| s2 | = |
(ii) Assume that the hay fever rate in each age group has an approximately
(a) What is the level of significance?
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