You wish to test the following daim (Ha) at a significance level of a = 0.01. H.:µ = 75.1 Ha:µ > 75.1 You believe the population is normally distributed and you know the standard deviation is o = 16.3. You obtain a sample mean of M = 77 for a sample of sizen = 47. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value - The p-value is... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final condusion is that... O There is sufficient evidence to warrant rejection of the daim that the population mean is greater than 75.1. O There is not sufficient evidence to warrant rejection of the daim that the population mean is greater than 75.1.
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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