Glucose Level: Horses –Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).938882105991108489The sample mean is x̄= 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from experience that σ = 12.5. The mean glucose level for the horse should be μ = 85. Does the data indicate that Gentle Ben has an overall glucose level higher than 85? Use α = 0.05. l)Compute the test statistic since σ is known: m)Find the P-Value associated with this z score and the indicated test. n)Determine if the P-Value is greater or less than the level of significance (α).o)Do you reject or fail to reject the null hypothesis? p)Is there sufficient or insufficient evidence to reject or fail to reject the claim that Gentle Ben’s average glucose level is higher than average?
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!
Glucose Level: Horses –Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).938882105991108489The sample mean is x̄= 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a
l)Compute the test statistic since σ is known:
m)Find the P-Value associated with this z score and the indicated test.
n)Determine if the P-Value is greater or less than the level of significance (α).o)Do you reject or fail to reject the null hypothesis?
p)Is there sufficient or insufficient evidence to reject or fail to reject the claim that Gentle Ben’s average glucose level is higher than average?
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