Researchers at a National Weather Center in the northeastern United States recorded the number of 90 degree days each year since records first started in 1875. The numbers form a normal shaped distribution with a mean of μ = 9 and a standard deviation of σ = 2.5. To see if the data showed any evidence of global warming, they also computed the mean number of 90 degree days for the most recent n = 4 years and obtained M = 11.7 days. Do the data indicate that the past four years have had significantly more 90 degree days than would be expected for a random sample from this populaton? Use a one-tailed test with alpha = .05.
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!
Researchers at a National Weather Center in the northeastern United States
recorded the number of 90 degree days each year since records first started in
1875. The numbers form a
standard deviation of σ = 2.5. To see if the data showed any evidence of global
warming, they also computed the mean number of 90 degree days for the most
recent n = 4 years and obtained M = 11.7 days. Do the data indicate that the past
four years have had significantly more 90 degree days than would be expected for a
random sample from this populaton? Use a one-tailed test with alpha = .05.
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