A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacteria. The table shows the results for the number of bacteria per cubic foot for both types of rooms. A normal probability plot and boxplot indicate that the data are approximately normally distributed with no outliers. Do carpeted rooms have more bacteria than uncarpeted rooms at the α=0.01 level of significance? Full data set Carpeted Uncarpeted 12.8 15.7 7 8.7 6.4 8 8.3 9.4 9.1 1.6 0.6 4.1 7.8 14.2 9.8 3 Use the t-table for reference. What are the null and alternative hypotheses?
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!
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A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacteria. The table shows the results for the number of bacteria per cubic foot for both types of rooms. A normal probability plot and boxplot indicate that the data are approximately
α=0.01
level of significance? |
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Full data set
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Carpeted
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Uncarpeted
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12.8
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15.7
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7
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8.7
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6.4
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8
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8.3
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9.4
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9.1
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1.6
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0.6
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4.1
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7.8
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14.2
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9.8
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3
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