Rosie is an aging sheep dog in Montana who gets regular checkups from her owner, the local veterinarian. Let x be a random variable that represents Rosie’s resting heart rate (in beats per minute). From past experience, the vet knows that x has a normal distribution with σ=12. The vet checked the Merck Veterinary Manual and found that for dogs of this breed, μ=115 beats per minute. Over the past 6 weeks, Rosie’s heart rate (beats/min) measured: 93, 109, 110, 89, 112, 117 The sample mean is x¯=105. The vet is concerned that Rosie’s heart rate may be slowing. Does the data indicate that this is the case? 1. When using α= 0.05 we would reject H0 because p-value< α. If we now think of using the spectrum mentioned on the previous page, how would we conclude our hypothesis test? 2. Using this new conclusion to the test, how would we interpret this conclusion in the context of the problem?
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!
(Image) This spectrum tells us that if our p-value is less than 0.01, we have convincing evidence to reject H0, if 0.01< p−value<0.05 we have moderate evidence to reject H0, and so on and so forth. Also if p-value<0.001 we might say we have very strong evidence to reject H0
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Rosie is an aging sheep dog in Montana who gets regular checkups from her owner, the local veterinarian. Let x be a random variable that represents Rosie’s resting heart rate (in beats per minute). From past experience, the vet knows that x has a
Over the past 6 weeks, Rosie’s heart rate (beats/min) measured:
93, 109, 110, 89, 112, 117
The sample mean is x¯=105. The vet is concerned that Rosie’s heart rate may be slowing. Does the data indicate that this is the case?
1. When using α= 0.05 we would reject H0 because p-value< α. If we now think of using the spectrum mentioned on the previous page, how would we conclude our hypothesis test?
2. Using this new conclusion to the test, how would we interpret this conclusion in the context of the problem?
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