Question

10. A statistics instructor is interested in comparing the final grades for his introductory course with the final grades for all of the introductory statistics courses at Brandon University in the past ten years. The final grades for his class form a normal distribution with a x= 75 and as= 10. The final grades for all of the introductory statistics courses also form a normal distribution, but with a u = 60 and a = 15. On the basis of the instructor's class size, he determines that om = 5. He determines that the mean final grade for his introductory statistics course has a corresponding z = +3.00. He concludes that the final grades for his introductory statistics course are not too different from the final grades for all of the introductory statistics courses in the past ten years. With this information in mind, please answer the following questions: a. In this scenario, what is the sample and what is the population? (2 points) b. What is the sample size? Show how you calculated it. "Hint: Think about the formula for each of the statistics that are provided above. (2 point) c. What is the representative value for the final grades in the sample? (1 point) d. On average, a student's final grade in the sample will deviate from sample mean by how many units? (1 point) e. In this scenario, the mean final grade for a sample is expected to deviate from the mean final grade in the population by how many units? (1 point) What is the probability of obtaining a sample mean as extreme as the one he obtained from the population? (1 point) g. Is the instructor justified in concluding that his final grades are not too different from the population? Why? (2 points) 11. For a normal distribution with u = 500 and o = 100, determine the following: a. A raw score of 700 corresponds to what value of z? (1 point) b. Az = -1.25 corresponds to what raw score? (1 point) c. What raw score separates the top 10% of the distribution from bottom 90%? (2 points) d. What scores form the boundaries for the middle 60% of the distribution? (3 points) e. What is the probability of randomly selecting a score greater than X = 475? (2 points) f. If every raw score was transformed into a Z-score, what would be the mean of the distribution of z-scores? Why? (1 point)

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Answer 1

10. (a) The sample is the final grade students in the class and the population is the final grades for all statistics courses.

(b) The test statistic, z = (x - µ)/σ/√n

3 = (75 - 60)/15/√n

n = 9

(c) The value is 75.

(d) On average, 10/√9 = 3 students will deviate from the sample mean by one unit.

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