Exam+-+I+%28BSTAT+3321%29_Set+A

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3321

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Statistics

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Feb 20, 2024

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Exam I BSTAT 3321 Last Name ........................................................... First Name .......................................................... ID# ...................................................................... Version 1 1

1) Alison has all her money invested in two mutual funds, A and B. She knows that there is a 30% chance that fund A will rise in price, and a 50% chance that fund B will rise in price given that fund A rises in price. What is the probability that both fund A and fund B will rise in price? A) 0.15 B) 0.31 C) 0.67 D) 1.00 2) There is a 25% chance that a customer who purchases milk will also purchase bread. The probability of a milk purchase is 70% and the probability of a bread purchase is 50%. What is the probability that a customer will purchase bread given that he/she buys milk? A) 50% B) 25% C) 36% D) 64% Version 1 2

3) Restaurants in London, Paris, and New York want diners to experience eating in pitch darkness to heighten their senses of taste and smell ( Vanity Fair , December 2011). Suppose 400 people were asked, “If given the opportunity, would you eat at one of these restaurants?” The accompanying contingency table, cross-classified by age, would be produced. 18–29 30–44 45–64 65+ Yes 50 39 76 65 No 50 61 24 35 Convert the contingency table to a joint probability table. 4) The variance and standard deviation are the most widely used measures of central location. ⊚ true ⊚ false Version 1 3

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5) The following data represent scores on a pop quiz in a statistics section. 36 66 72 86 82 38 55 63 31 80 72 55 90 22 27 66 68 48 42 30 Suppose the data on quiz scores will be grouped into five classes. The width of the classes for a frequency distribution or histogram is the closest to __________. A) 14 B) 16 C) 10 D) 12 6) For a categorical variable, a frequency distribution groups its values into __________ and records the number of __________. 7) What graphical tool is best used to display the relative frequency of a numerical variable? A) Pie chart B) Bar chart C) Histogram D) Ogive Version 1 4

8) Suppose that 60% of the students do homework regularly. It is also known that 80% of students who had been doing homework regularly, end up doing well in the course. Only 20% of students who had not been doing homework regularly end up doing well in the course. Given that a student did well in the course, what is the probability that the student had been doing homework regularly? A) 0.143 B) 0.429 C) 0.857 D) 0.286 9) You buy 50 stocks of Company A, 30 of Company B, and 20 of Company C. The annual returns of these companies are 8%, 12%, and 10% respectively. The average return for one year is the closest to __________. A) 10.0% B) 9.6% C) 10.5% D) 9.1% Version 1 5

10) Let , and . Compute . A) 0.5 B) 0.67 C) 0.45 D) 0.33 11) The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. Chocolate Vanilla Swirl Under 25 years old 40 20 15 At least 25 years old 15 40 20 What is the probability a randomly selected customer prefers chocolate given he or she is at least 25 years old? A) 0.27 B) 0.77 C) 0.20 D) 0.10 Version 1 6

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12) Calculate the mean, median, and mode of the sample data below. 6 3 9 5 3 7 8 1 Version 1 7

13) Each month the Bureau of Labor Statistics reports the number of people (in thousands) employed in the United States by age. The accompanying frequency distribution shows the results for August. Age Frequency 16 to 19 4,794 20 to 24 13,273 25 to 34 30,789 35 to 44 30,021 45 to 54 32,798 55 and over 28,660 a. Construct a relative frequency distribution. What proportion of workers is between 20 and 24 years old? b. Construct a cumulative relative frequency distribution. What proportion of workers is younger than 35 years old? Version 1 8

14) The complement of an event A , denoted by A C , within the sample space S , is the event consisting of all outcomes of A that are not in S . ⊚ true ⊚ false 15) The following data represent monthly returns (in percent): −7.24 1.64 3.48 −2.49 9.30 The geometric mean return is the closest to __________. A) 0.94% B) −0.43% C) 0.78% D) 4.79% 16) The two branches of the study of statistics are generally referred to as A) inferential and differential statistics. B) descriptive and referential statistics. C) descriptive and inferential statistics. D) differential and descriptive statistics. Version 1 9

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17) The following table summarizes the ages of the 400 richest Americans. Suppose we select one of these individuals. Find the probability that the selected individual is less than 80 years old. Ages Frequency less than 40 7 40 up to 50 47 50 up to 60 90 60 up to 70 109 70 up to 80 93 80 up to 90 45 90 or more 9 Version 1 10

Answer Key Test name: Exam - I (BSTAT 3321) 1) A The conditional probability is calculated as Given: P ( A ) = 0.30 and P ( B|A ) = 0.50 P ( A ∩ B ) = P ( A|B ) × P ( B ) = P ( B|A ) × ( A ) = 0.50 × 0.30 = 0.15. 2) C P(milk and bread) = 0.25; P(milk) = 0.7; P(bread) = 0.5. P(bread | milk) = P(milk and bread)/P(milk) = 0.25/0.7 = 36%. 3) Short Answer 18–29 30–44 45–64 65+ Total Yes 0.125 0.975 0.19 0.1625 0.575 No 0.125 0.1525 0.06 0.0875 0.425 Total 0.250 0.250 0.250 0.250 1.000 A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table. 4) FALSE The variance and standard deviation are the most widely used measures of dispersion. 5) A Class width = (Maximum − Minimum)/(Number of classes) = (90 −22)/5 = 13.60 ≈ 14 (We always round up.) 6) [categories, observations] For qualitative data, a frequency distribution groups data into categories and records the number of observations that fall into each category. 7) C Histograms are used to display the relative frequency of a numerical variable. An ogive is used to display the cumulative frequency, while the bar chart and pie chart display qualitative data. Version 1 11

8) C The total probability rule conditional on two events B and B c is defined as Conditional probability is computed as Given:  P(Homework) = 0.60  P(Well|Homework) = 0.80  P(Well|Not Homework) = 0.20 9) B The mean for a frequency distribution is defined as where is the relative frequency of the interval and is the midpoint of the interval. 10) B The total probability rule conditional on two events B and B c is defined as . 11) C A contingency table shows frequencies for two qualitative or categorical variables, x and y , where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table. 12) Short Answer Mean = 5.25, Median = 5.5, Mode = 3 Version 1 12

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The sample mean is computed as The median is the middle value of a data set. The mode is the most frequently occurring value in a data set. 13) Short Answer a. 0.095. b. 0.348. Age Frequency Relative Frequency Cumulative Relative Frequency 16 to 19 4,794 0.034 0.034 20 to 24 13,273 0.095 0.129 25 to 34 30,789 0.219 0.348 35 to 44 30,021 0.214 0.562 45 to 54 32,798 0.234 0.796 55 and over 28,660 0.204 1.000 14) FALSE A c consists of all outcomes of S that are not in A . 15) C =GEOMEAN(1−0.0724,1+0.0164,1+0.0348,1−0.0249,1+0.0930)−1 = 0.78% The geometric mean return is defined as Wrong answers include arithmetic mean, median, using positive values of growth rates instead of negative ones, and not converting percentages to fractions. 16) C The two branches of statistics are descriptive and inferential statistics. 17) Short Answer 0.865 Version 1 13