Final Exam Problems - Introduction to Statistics - 2011 | STAT 1222, Exams of Statistics

Download Final Exam Problems - Introduction to Statistics - 2011 | STAT 1222 and more Exams Statistics in PDF only on Docsity! STAT 1222 FINAL EXAM FALL 2001 Use the following to answer questions 1, 2 and 3. A random sample of six families has the following number of children: 0,1,3,6,4,1 1) The mean number of children in this sample is closest to a) 1 b) 6 c) 2.5 d) 2 e) none of the above 2) The median number of children is closest to a) 1 b) 5.099 c) 4.5 d) 2 e) none of the above 3) The standard deviation for this sample is closest to a) 3 b) 2.258 c) 5.099 d) 2 e) none of the above 4)The starting annual salaries for a sample of 30 liberal-arts graduates is given by the following frequency histogram Starting salary ($1000) Frequency 22 – 24 3 25 – 27 8 29 – 31 7 32 – 34 4 35 – 37 6 38 – 40 2 the cumulative frequency for the class 32-34 is a) 18 b) 4 c) 8 d) 12 e) 22 Use the following to answer questions 5 and 6 In a survey, 90 dog owners were asked two questions: (1) how much did you spend on your dog’s health care last year? (2) is your dog purebred or mixed breed? The responses to the questions are summarized in the following table. Type of Dog Purebred Mixed Breed Health Care cost Less than $100 19 21 $100 or more 35 15 STAT 1222 FINAL EXAM FALL 2001 5) The probability that $100 or more was spent on a dog’s health care last year, is closest to a) 0.556 b) 0.444 c) 0.389 d) 0.167 e) 0.600 6) The probability that the dog was of mixed breed, given that a dog owner spent less than $100 on the dog’s health care is closest to a) 0.475 b) 0.210 c) 0.400 d) 0.525 e) none of the above 7) Let Z be the standard normal random variable. Then P (Z > 0.93) is closest to, a) 0.1762 b) 0.3238 c) 0.8238 d) 0.6762 e) none of the above Use the following to answer questions 8 and 9 As reported by the U.S. National Center for Health Statistics in Vital and Health Statistics, males who are 6 ft tall and between 18 and 24 years of age have a mean weight of 175 lb. If the weights are normally distributed with a standard deviation of 14 lb, 8) The probability that such a male will weigh more than 150 lb is closest to, a) 0.9633 b) 0.0367 c) 0.5367 d) 0.4633 e) none of the above 9) The probability that such a male will weigh between 190 and 210 is closest to, a) 0.9938 b) 0.8577 c) 0.0062 d) 0.1423 e) 0.1361 10) As reported by Television Bureau of Advertising, Inc., in Trends in Television, 80% of U.S. households have a VCR. If six households are randomly selected, the probability that exactly four households have a VCR is closest to, a) 0.754 b) 0.246 c) 0.082 d) 0.343 e) 0.097 11) Consider the scatterplot below. A plausible value for the correlation between X and Y is a) +0.1 b) +0.9 c) –1.0 d) +1.0 e) –0.8 STAT 1222 FINAL EXAM FALL 2001 18) Choose the appropriate hypotheses to test the Bureau’s claim a) 0H : µ1 = µ2 versus aH : µ1 ≠ µ2 b) 0H : µ1 ≥ µ2 versus aH : µ1 < µ2 c) 0H : µ1 ≤ µ2 versus aH : µ1 > µ2 d) 0H : 1x ≤ 2x versus aH : 1x > 2x e) 0H : 1x ≥ 2x versus aH : 1x < 2x 19) Find the values of the test statistic a) 4.06 b) 8.87 c) –8.87 d) 2.33 e) –4.06 Use the following for exercises 20 and 21 The per capita consumption of soft drinks per year by Americans in a recent study was normally distributed, with a mean of 51.2 gallons and a standard deviation of 17.1 gallons. A random sample of size 25 is drawn from this population. 20) The mean and standard error of X is closest to a) 51.2 x µ = and 3.42 x σ = b) 51.2 x µ = and 11.70 x σ = c) 2.05 x µ = and 3.42 x σ = d) 51.2 x µ = and 17.1 x σ = e) 51.2 x µ = and 0.684 x σ = 21) The approximate probability that in a random sample of 25 Americans, the mean per capital consumption exceeds 55 gallons is, a) 0.3665 b) 0.8665 c) 0.1335 d) 0.5335 e) none of the above Use the following for questions 22 and 23 A major insurance company wants to relate the amount of fire damage y (in thousands of dollars) in major residential fires to the distance x (in miles) between the burning house and the nearest fire station. Data from a random sample of 15 such fires was used to establish the following regression model ˆ 10.28 4.92 , andy x= + 2 0.9235r = 22)The predicted fire damage, if a major residential fire were to occur 3.5 miles from the nearest fire station, is closest to, in thousands of dollars, a) 10.28 b) 17.22 c) 27.50 d) 3.23 e) can not be determined STAT 1222 FINAL EXAM FALL 2001 23) Which of the following is true? a) there is a weak linear correlation between fire damage and distance of the house from the nearest fire station b) The further away that the burning house is from the nearest fire station the less the damage c) The coefficient of correlation is approximately 0.96 d) For each mile that the burning house is further away from the nearest fire station, the average fire damage decreases by 4.92 thousand dollars e) None of the above 24) The financial aid officer at a particular university wishes to estimate the mean cost of textbooks for students. For the estimate to be useful, it should be within $20 of the true population mean. The standard deviation is assumed to be $100. The sample size required for this experiment to be 90% confident of achieving this level of accuracy is closest to a) 42 b) 97 c) 136 d) 68 e) 166 25) A certain population follows a normal distribution with mean µ and a standard deviation σ=2.5. Suppose that we draw a random sample of 50 observations and test, at α=0.05, Ho: µ = 10 vs Ha: µ > 10. Which of following is the correct rejection region? a) Reject 0H if 1.96z > b) Reject 0H if 1.645z < c) Reject 0H if 1.282z > d) Reject 0H if 2.326z > e) Reject 0H if 1.645z > STAT 1222 FINAL EXAM FALL 2001 PART II 1. The table below displays data on age and price for a sample Orion vehicles Age (yrs) Price ($100s) _____________________ x y x = 58, y = 975, xy = 4732, 5 85 4 103 x2 = 326, y2 = 96129 6 70 5 82 5 89 5 98 6 66 6 96 2 169 7 70 7 48 a) (6pts) Estimate the linear regression line of Y on X b) (3pts) Compute the coefficient of correlation and interpret its value c) (5 pts) Is there sufficient evidence to conclude that there is a significant linear correlation between age of the Orion and price? Use α =0.05 d) (4pts) Find a 95% confidence interval for the mean price of an Orion, which is 3 years old. Interpret your result in the context of the problem.