High Temperatures in January Daily weather observations for southwestern Pennsylvania for the first three weeks of January show daily high temperatures as follows in degrees Fahrenheit: 57 28 39 28 37 30 55 35 44 59 51 60 46 62 51 37 46 51 The normal standard deviation in high temperatures for this time period is usually no more than 8 degrees. A meteorologist believes that with the unusual trend in temperatures the standard deviation is greater. At =α0.01 , can we conclude that the standard deviation is greater than 8 degrees? Assume the variable is normally distributed. (a)State the hypotheses and identify the claim with the correct hypothesis. :H0 ▼(Choose one) :H1 ▼(Choose one) This hypothesis test is a ▼(Choose one) test. (b)Find the critical value(s). Round the answers to three decimal places, if necessary. If there is more than one critical value, separate them with commas. Critical value(s): (c)Compute the test value. Round the sample standard deviation to three decimal places and the final answer to three decimal places. =χ2
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!
High Temperatures in January Daily weather observations for southwestern Pennsylvania for the first three weeks of January show daily high temperatures as follows in degrees Fahrenheit:
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57
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28
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39
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28
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37
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30
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55
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35
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44
|
59
|
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51
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60
|
46
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62
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51
|
37
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46
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51
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|
:H0 ▼(Choose one)
:H1 ▼(Choose one) This hypothesis test is a ▼(Choose one) test. |
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=χ2
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▼(Choose one) the null hypothesis.
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| There ▼(Choose one) enough evidence to support the claim that the standard deviation is greater than
8 degrees.
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