Invitational Mathematics Competition. Statistics Individual Test

Transcription

1 Invitational Mathematics Competition Statistics Individual Test December 12,

2 MULTIPLE CHOICE. If you think that the correct answer is not present, then choose 'E' for none of the above. 1) What level of measurement classifies data into mutually exclusive categories in which no order or ranking can be imposed on the data? A) ratio B) ordinal C) interval D) nominal 2) What type of sampling is being employed if the country is divided into economic classes and a sample is chosen from each class to be surveyed? A) stratified sampling B) random sampling C) systematic sampling D) cluster sampling 3) The following frequency distribution presents the frequency of passenger vehicles that pass through a certain intersection from 8:00 AM to 9:00 AM on a particular day. 1) 2) 3) Vehicle Type Frequency Motorcycle 8 Sedan 87 SUV 88 Truck 31 Construct a relative frequency distribution for the data. A) Vehicle Type Relative Frequency Motorcycle 0.08 Sedan 0.87 SUV 0.88 Truck 0.31 B) Vehicle Type Relative Frequency Motorcycle Sedan SUV 1 Truck

3 C) Vehicle Type Relative Frequency Motorcycle 0.037% Sedan 0.407% SUV 0.411% Truck 0.145% D) Vehicle Type Relative Frequency Motorcycle Sedan SUV Truck ) Box A contains the numbers 1, 2, 3, and 4. Box B contains the numbers 5, 6, 7, and 8. A number is first drawn from Box A and then another number from Box B. Using the figure below, how many outcomes are possible if both numbers are even? 4) A) 6 B) 16 C) 4 D) 8 5) The size of the box in a boxplot shows the of the data set. A) variance B) interquartile range C) skewness D) difference between the mean and the median 5) 3

4 6) The average weekly earnings in dollars for various industries are listed below. Find the percentile rank of , 683, 604, 706, 649, 729, 800, 547, 821, 851 A) 40th B) 35th C) 25th D) 45th 7) For the data set below, find the IQR. 6) 7) A) 13 B) 74 C) 65 D) 9 8) Given that the mean of a set of data is 25 and the standard deviation is 3, what is the coefficient of variation? A) 8.33 B) 0.12 C) 833% D) 12% 9) Approximate the sample standard deviation given the following frequency distribution. 8) 9) Class Frequency A) B) C) 22.4 D)

5 10) The following data represent the total price, in dollars, of 20 randomly-selected gasoline purchases at a certain convenience store. 10) Find the median price for these purchases. A) $37.70 B) $26.11 C) $36.67 D) $ ) A random sample of weights (in carats) of sapphires in a jeweler's collection is shown. Find the mean of the sample. 11) Class Boundaries Frequency A) B) 5.55 C) 5.95 D) ) Given the following frequency distribution, how many pieces of data were less than 28.5? Class Boundaries Frequencies A) 44 B) 25 C) 12 D) 13 12) 5

6 13) The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first grade class is shown below. 13) Number of cartoons watched X Probability P(X) What is the mean of the data? A) 1.18 B) 1.37 C) 1.89 D) ) Give the variance of the following distribution. 14) X P(X) A) 1.31 B) 1.25 C) 1.71 D) ) An investor is considering a $25,000 investment in a start-up company. She estimates that she has probability 0.05 of a $20,000 loss, probability 0.2 of a $20,000 profit, probability 0.15 of a $35,000 profit, and probability 0.6 of breaking even (a profit of $0). What is the expected value of the profit? A) $8250 B) $11,667 C) $10,250 D) $23,250 15) 6

7 16) In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths of a second. The results are presented in the following table. 16) Visual Auditory Compute the least-squares regression line for predicting auditory response time (y) from visual response time (x). A) y = x B) y = x C) y = x D) y = x 17) Compute the value of the correlation coefficient. x y A) B) C) D) ) In a simple random sample of size 88, there were 22 individuals in the category of interest. It is desired to test H 0 : p = 0.31 versus H 1 : p < Compute the test statistic z. A) 4.97 B) 0.25 C) 0.05 D) ) 18) 7

8 19) The mean annual tuition and fees for a sample of 12 private colleges was $36,800 with a standard deviation of $5000. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $33, ) Compute the value of the test statistic and state the number of degrees of freedom. A) 2.148; 11 degrees of freedom B) 2.148; 12 degrees of freedom C) 0.620; 12 degrees of freedom D) 0.620; 11 degrees of freedom 20) A recent study of business travelers claims they spend an average of $41.00 per day on meals. As a test of this claim, a random sampling of 16 business travelers found they had spent an average of $45.00 per day with a standard deviation of $3.65. What are the critical values for a two-tailed t test of this claim with α = 0.05? A) ±2.120 B) ±1.753 C) ±1.746 D) ± ) A test is made of H 0 : µ = 60 versus H 1 : µ > 60. A sample of size n = 77 is drawn, and x = 64. The population standard deviation is σ = 23. Compute the value of the test statistic z and determine if H 0 is rejected at the α = 0.05 level. A) 0.17, H 0 rejected B) 1.53, H 0 rejected C) 0.17, H 0 not rejected D) 1.53, H 0 not rejected 20) 21) 22) A report states that 38% of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 6 percentage points with 98% confidence? A) 276 B) 105 C) 356 D) ) 8

9 23) A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse? A) < p < B) < p < C) < p < D) < p < ) 7 squirrels were found to have an average weight of 8.7 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight. A) 8.3 < µ < 9.1 B) 6.0 < µ < 11.4 C) 7.9 < µ < 9.5 D) 7.7 < µ < ) A student looked up the number of years served by 35 of the more than 100 Supreme Court justices. The average number of years served by those 35 justices was If the standard deviation of the entire population is 7.3 years, find the 95% confidence interval for the average number of years served by all Supreme Court justices. A) 12.6 < µ < 15.0 B) 11.8 < µ < 15.8 C) 11.4 < µ < 16.2 D) 12.2 < µ < ) The average diameter of sand dollars on a certain island is 3.00 centimeters with a standard deviation of 1.00 centimeters. If 9 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 2.60 centimeters. Assume that the variable is normally distributed. A) B) C) D) ) If the standard deviation of a normally distributed population is 55.0 and we take a sample of size 25, then the standard error of the mean is A) 5.0 B) 2.2 C) 55.0 D) ) 24) 25) 26) 27) 9

10 28) A student takes a 5 question multiple choice quiz with 4 choices for each question. If the student guesses at random on each question, what is the probability that the student gets exactly 3 questions correct? A) B) C) D) ) At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years, and the distribution is approximately normal. If an employee is picked at random, what is the probability that the employee has worked at the store for over 10 years? A) 1.7% B) 99.2% C) 0.8% D) 49.2% 30) A bottler of drinking water fills plastic bottles with a mean volume of 998 milliliters (ml) and standard deviation 7 ml. The fill volumes are normally distributed. What proportion of bottles have volumes greater than 999 ml? A) B) C) D) ) 29) 30) 10

11 Answer Key Testname: STATS INDIVIDUAL 1) D 2) A 3) D 4) C 5) B 6) B 7) D 8) D 9) D 10) A 11) D 12) B 13) D 14) C 15) A 16) B 17) C 18) D 19) A 20) D 21) D 22) C 23) A 24) D 25) C 26) A 27) D 28) B 29) C 30) A 11