Math sample final exam without solutions | MATH 2300, Exams of Data Analysis & Statistical Methods

Download Math sample final exam without solutions | MATH 2300 and more Exams Data Analysis & Statistical Methods in PDF only on Docsity! MATH 2300 – Sample Final Exam – Summer 2005 Show all the details leading to the solution of a problem, and explain your answers. Use enough significant decimal digits so that you get a precise answer. All problems are weighted equally. 1. Consider the following data: 11 20 62 61 7 4 5 25 24 32 12 21 2 2 34 31 45 55 56 44 11 11 12 33 35 3 4 14 24 54 (a) Construct a stem-and-leaf diagram of the above data. Using the plot, find the median, the quartiles, the interquartile range, and the range of the data. (b) Construct a histogram of the above data. 2. A data set consists of the following observations: −2, 3, 3,−2,−4,−9, 9, 9,−2, 2. (a) Find the sample standard deviation. (b) Find the sample median, the first quartile, and the third quartile. (c) Find the sample range and the sample interquartile range. (d) Construct a boxplot of the above data. 3. Suppose that a student’s math score X from next year’s Graduate Record Exam can be considered as an observation from a normal population having mean 467 and standard deviation 110. Find the probability that the student scores are between 290 and 500. Show all work and use the appropriate notation. 4. Suppose A and B are events such that P (A) = .4 and P (B) = .25. (a) Determine P (A ∪B) if A and B are independent. (b) Determine P (A ∪B) if A and B are mutually exclusive. 5. Each year, an insurance company reviews its claim experience in order to set failure rates. Regarding their damage-only automobile insurance policies, at least one claim was made on 2,073 of the 12,299 policies in effect for the year. Treating these data as a random sample from the population of all possible damage- only policies that could be issued, estimate the population proportion of at least one claim and give an 88% confidence interval for this proportion. Use the proper notation, and show all work. 1 6. For two events A and B, if P (A) = .4, P (B) = 0.35, and P (A|B) = .5, find (a) P (A|B); (b) P (B|A). 7. Consider the following discrete probability distribution of a random variable X: x −3 −2 2 4 f(x) 0.11 0.33 0.26 0.30 (a) Find P (X ≤ −1) and P (−2 ≤ X < 4). (b) Find the (theoretical) standard deviation of X. 8. The distribution for the time it takes a professor to grade a 50-minute exam of a (typical) student has a mean of 20 and a standard deviation of 18 minutes. For a random sample of 44 exams find P (15 < X < 23), where X is the sample mean. Show all work and use the appropriate notation. 9. A sample of 36 measurements provide the sample mean x = 11.38 and the sample standard deviation s = 5.43. For the population mean, construct a 92% percent confidence interval. Show all work and use the appropriate notation. 10. The following data come from a normal distribution: 2, 3, 2, 8, 4, 7. Test the hypothesis H0 : µ = 6 against H1 : µ < 6 at α = .01. What are the assumptions for this hypothesis test? 11. Breakfast cereals from three leading manufacturers can be classified either above average or below average in sugar content. Data for twelve cereals from each manufacturer are given below: Below Average Above average Total General Mils 4 8 12 Kellogg 5 7 12 Quaker 7 5 12 Total (a) Complete the marginal totals. (b) Calculate the relative frequencies separately for each row. (c) Comment on any apparent differences between the cereals produced by the three companies. 12. An investigation is conducted to determine if the mean age of welfare recipients differs between two cities A and B. Random samples of 75 and 100 welfare recipients are selected from city A and city B, respectively, and the following calculations were made: xA = 37.8, xB = 43.2, sA = 6.8, sB = 7.5. (s here denotes standard deviation.) (a) Do the data provide strong evidence that the mean ages are different in city A and city B? Test at α = .02. 2