A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on da from the administrator of the exam, scores are normally distributed with u = 514. The teacher obtains a random sample of 1800 students, puts them through the reu class, and finds that the mean math score of the 1800 students is 521 with a standard deviation of 113. Complete parts (a) through (d) below. OC. Ho p>514, H,: u#514 O D. Ho =514, H,: p#514 (b) Test the hypothesis at the = 0.10 level of significance. Is a mean math score of 521 statistically significantly higher than 514? Conduct a hypothesis test using the P-value approach. Find the test statistic. to = 2.63 (Round to two decimal places as needed.) Find the P-value. The P-value is (Round to three decimal places as needed.)
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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