DE CHAZAL DU MEE BUSINESS SCHOOL AUGUST 2003 MOCK EXAMINATIONS STA 105-M (BASIC STATISTICS) READ THE INSTRUCTIONS BELOW VERY CAREFULLY.

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1 DE CHAZAL DU MEE BUSINESS SCHOOL AUGUST 003 MOCK EXAMINATIONS STA 105-M (BASIC STATISTICS) Time: hours READ THE INSTRUCTIONS BELOW VERY CAREFULLY. Do not open this question paper until you have been told to do so by the invigilator. This is a MULTIPLE-CHOICE paper with 5 questions. No negative marking will apply. Each question carries FOUR marks. Silent and non-programmable calculators may be used. The total number of marks available is 100. ANSWER ALL QUESTIONS. This question paper consists of NINE printed pages.

2 QUESTION 1 Consider the following random variables: A: Type of personal computer purchased by a customer B: The country of manufacture of the next automobile to pass through a given intersection. C: Price of a textbook. D: The type of racket used by a randomly selected player at a tennis tournament. Which one of the variables is a quantitative variable? (1) Only A () Only B (3) Only C (4) Only D (5) None of the above QUESTION The following is a sample of ages of individuals working at home: The interquartile range of this sample is: (1) 36 () 48,5 (3) 5,5 (4) 19 (5) 38,5 QUESTION 3 Consider the following statements: A: Open-ended questions are good for exploratory research. B: Anonymity is especially necessary if there are sensitive questions in the questionnaire. C: Open-ended questions are an easy option for a statistician. D: In a pilot study leading questions are acceptable. Which statements are correct? (1) A and B () A and C (3) B and C (4) B and D (5) A, B and D Examiner: Mr. Gamal Ballam STA 105-M August-003

3 3 QUESTION 4 If a random sample of 50 observations is drawn from a population with mean of 78 and population variance of 31, what is the standard deviation of the sample mean? (1) 0,7874 () 0,637 (3) 0,7954 (4) 0,600 (5) 0,5570 QUESTION 5 Events A and B are independent. If P(A) 0.3 and P(B) 0.6, P(A or B) is equal to (1) 0.9 () 0.5 (3) 0.1 (4) 0.18 (5) 0.7 Use the following information for questions 6 to 8. A large company stratified their employees into 5 strata: Stratum sizes N 1 60 N 0 N N 4 00 N Stratum variances σ 3 σ 5 σ 4 σ 8 σ A sample of 100 is to be selected. QUESTION 6 Determine n 1 according to the equal allocation. (1) 19 () 0 (3) 1 (4) 15 (5) 16 Examiner: Mr. Gamal Ballam STA 105-M August-003

4 4 QUESTION 7 Determine n 4 according to the proportional allocation (correct to the nearest integer). (1) 0 () 16 (3) 17 (4) 19 (5) 30 QUESTION 8 Determine n 3 according to the optimal allocation (correct to the nearest integer). (1) 17 () 8 (3) 5 (4) 14 (5) 30 QUESTION 9 A random sample of people inoculated against influenza, showed the following results. Inoculated Not inoculated Got influenza 3 7 Didn t get influenza 8 4 The probability that a person caught influenza, given he/she has been inoculated, is (1) () 0.5 (3) 0.77 (4) (5) QUESTION 10 If Z ~ N(1.5, 1) and the standard deviation of the means of samples of size n from the population is 0.5, what is the value of n? (1) 6 () 4 (3) 7 (4) 36 (5) 48 Examiner: Mr. Gamal Ballam STA 105-M August-003

5 5 QUESTION 11 If Z ~ N(0, 1), the probability that -3. < Z < 1.5 is equal to (1) () (3) (4) (5) QUESTION 1 A simple random sample of 16 radio stations is selected in order to estimate the average charge for the same fixed-length spot announcement. The sample mean is 17.1 and variance is A 95% confidence interval for fixed-length spot announcement is calculated as (1) (117,0048; 137,195) () (14,356; 19,844) (3) (116,14; 138,076) (4) (14,067; 130,1733) (5) (65,6344; 188,5656) QUESTION 13 Two events A and B are such that P(A) ¼, P(B) ¾ and P(A and B) 1/8. What is the value of P(A B )? (1) ¾ () 7/8 (3) 1/6 (4) ½ (5) 1/8 QUESTION 14 Consider the following 3 statements in connection with the confidence interval for mean µ of a population. A: The confidence interval for mean µ can be made narrower by increasing the sample size. B: If such an interval is too narrow, it can be caused by the critical t-value being too small. C: If such an interval is too wide, it may be that the sample standard deviation is too small. Which of the following statements are incorrect? (1) Only A () Only B (3) Only C (4) More than one statement is incorrect (5) All 3 statements are incorrect. Examiner: Mr. Gamal Ballam STA 105-M August-003

6 6 QUESTION 15 The body mass (in grams) of 70 different species of birds in a certain area were measured with 8.6 the smallest mass and 48.5 the largest mass. If these measurements are represented in a frequency table, where all the intervals are of the same length, the length suggested by Sturges rule for each class interval is (1) 5 () 6 (3) 39.9 (4) 3 (5) 15.0 QUESTION 16 An apple is picked at random from a certain tree. The probability that it is ripe is 0.6 and the probability that it has worms is 0.3. Only ripe apples can have worms. What is the probability the apple will be edible (i.e., ripe and without worms)? (1) 0.3 () 0.5 (3) 0.1 (4) 0.4 (5) 0.9 QUESTION 17 The 99% limits for an individual observation from the same population as the following random sample of test marks is given as (1) 5,00 < X < 107,00 () 0,95 < X < 10,05 (3) 1,93 < X < 111,07 (4) 0,95 < X < 10,05 (5) 1,93 < X < 111,07 Examiner: Mr. Gamal Ballam STA 105-M August-003

7 7 QUESTION 18 The sample mean X is called an unbiased estimator for the population mean because (1) S 1 n ( X i X ) n 1 i 1 () E (µ) X (3) Var( X ) (4) E( X ) µ σ σ (5) Var (µ) n n QUESTION 19 A new treatment was used on patients afflicted by a certain disease. Of a total of 00 patients afflicted with the disease, 10 were treated with this method of whom 1 died. 160 of the patients recovered. What is the conditional probability that patients who had not treated, recovered? (1) 0.65 () 0.80 (3) 0.54 (4) 0.60 (5) QUESTION 0 The ages of the population of staff at a company are normally distributed. A random sample of 5 members of staff at this company was drawn with men 41 and variance 4 and their ages were noted. To calculate a 90% confidence interval for the age of a member of staff at this company, the critical value is (1) () 1.96 (3) (4) (5) Examiner: Mr. Gamal Ballam STA 105-M August-003

8 8 QUESTION 1 Consider the following statements: A: An unbiased estimator for a parameter should always be close to the actual value of the parameter B: An unbiased estimator for a parameter should on average (over a large number of samples) be close to the actual value of the parameter C: An unbiased estimator for a parameter should have a small variance Which statement(s) is (are) correct? (1) Only A () Only B (3) Only C (4) None (5) More than one is correct QUESTION Consider the following statements: A: The aim of stratification is to decrease the variance of the sample mean. B: The optimal allocation of sample units to strata is the one that will make the variance of the estimator of the population mean a minimum C: Optimal allocation means that the largest samples will be taken from the strata with the smallest variance D: Stratification serves to ensure that the sample is representative Which of the statements above is/are incorrect? (1) Only A () Only B (3) Only C (4) Only D (5) More than one is incorrect Examiner: Mr. Gamal Ballam STA 105-M August-003

9 9 QUESTION 3 An unbiased estimator for σ x is (1) () (3) (4) (5) N N 1 S N 1 σ N N 1 S N N 1 S n N 1 σ n QUESTION 4 Which one of these variables is not continuous? (1) The amount of fuel (in litres) left in a particular car s fuel tank () The number of boys who play football (3) The height (in cm) of a large building (4) The distance (in km) between a train station and a school (5) The area in a province planted with grapes QUESTION 5 The monthly salaries of 0 employees of a company are displayed below: Which one of the following is an outlier? (1) 6000 () 10,000 (3) 7500 (4) 800 (5) 900 END OF PAPER Examiner: Mr. Gamal Ballam STA 105-M August-003