In Izmir University of Economics, a statistics instructor is interested in the ability of students to assess the difficulty of a test they have taken in the statistic course. This test was taken by a large group of students in the course, and the average score was 94.4. A random sample of eight students was asked to predict this average score. Their predictions are shown below. Assuming a normal distribution, test the null hypothesis that the population mean prediction would be 94.4. Use a two-sided alternative and a 5% significance level. 74 81 75 66 62 72 99 82 D Click the icon to view the upper critical values of the Student's t distribution. What are the null and alternative hypotheses for this test? ΟΑ. H, μ2 944 H, p<94.4 O B. H u#94.4 H, u= 94.4 O D. H, us94.4 OC. H; p= 94.4 H p#94.4 H, p> 94.4 For this test at the significance level a with sample mean x, hypothesized mean H. Ssample standard deviation s, and sample size n, what is the form of the decision rule? x-Ho O A. Reject H, if x-Ho >h-1.a/2 s/ n <-4-1a/2 or reject H, if s/ yn x-Ho O B. Reject H, if <-4-1,a
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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