Exam #1. Good luck! Page 1 of 7

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1 Exam # Total: 00 points Date: July, 008 Time: :00 :0 You have hour and 0 minutes to finish the exam. Please read the question carefully and assign your time smartly. Please PRINIT your name on each page of the exam sheet. Good luck! Page of 7

2 Bus 0 Exam #. True/False Questions (*=0 points. Circle the right answer.) ) The data downloaded from an official website (e.g. ) are primary data because the data reflects the population. ) To determine whether the data is for population or sample, we have to know the subject of interest. For example, the starting salaries of all the business graduates at CSUSM are considered population data in a report for CoBA CSUSM, but can be considered as a set of sample data for all the business graduates nation-wide. ) A group of students need to conduct a suvey on cell phone users preferences to complete their marketing project. They control their sample distribution to contain 0% users from <0 age group, 0% users from 0~0 age group, 0% users from 0~0 age group, and 0% users from >0 age group. The sampling method to control such a distribution is called the systematic sampling technique. Comment [f]: From website secondary. Primary is only when you obtain it yourself. Comment [f]: Whether data is population or sample depends on the subject. If the data cover all the items concerned, then it s population. Comment [f]: The described is stratified sampling, not systematic. ) We assume x is of Poisson distribution when x represents the number of successes in a fixed number of trials, where the probability of success is the same in each trial. (Skipped) ) In the experiement of drawing a card out of the a bridge deck, let E= the card is red and E= the card is a Ace. We can conclude that E and E are mutually exclusive.. Multiple Choices (*= points. Only one of the answer is correct.) ) If use a systematic random sampling technique to select a sample of size 0 from a population with,000 items, the first item selected from the ordered population will be ( B ) A) randomly selected between and 0. B) randomly selected between and 0. C) any randomly selected value between and,000. D) item 0 or 0. Comment [f]: If E happens, (or say that the card is red), the card can still be Ace. So they are not mutually exclusive. Comment [f]: The first number (random start) should be between the interval. Interval in this case is 000/0 = 0. ) Student ID number are data. ( A ) A) nominal B) ratio C) interval D) ordinal Page of 7

3 Bus 0 Exam # ) Which of the following game is a fair game? (A game is defined as fair if the expected gain of playing a game is 0) ( A ) A) Throwing one die. If the number on the die is or higher, then player wins and get $00; otherwise the player loses $00. B) Throwing one die. If the number on the die is or higher, then player wins and get $00; otherwise the player loses $00. C) Throwing one die. If the number on the die is or higher, then player wins and get $00; otherwise the player loses $00. D) All of the above games are fair. ) A couple bought a -bedroom house at $70,000 in Rancho Bernardo area. The wife was complaining that they have paid too much for a bedroom house. The husband is trying to show her that the price is reasonable, which of the following statement helps the husband? ( B ) A) The variance of a -bedroom house price is 0,000,000,000. Comment [f6]: P(win) = P (,, 6) = ½; P (lose) = -P(win) = ½ E(x) = 00*/ + (-00)*/ = 0 Comment [f7]: P(win) = P (, 6) = /6 = / ; P (lose) = -P(win) = / E(x) = 00*/ + (-00)*/ < 0 Comment [f8]: P(win) = P (,,, 6) = ½; P (lose) = -P(win) = ½ E(x) = 00*/ + (-00)*/ = 0 Comment [f9]: Only Mean shows central distribution. The others measures spread. B) The mean price for a -bedroom in the area is $800,000. C) The standard deviation of a -bedroom house price is $00,000. D) The interquartile range of a -bedroom house price is $00,000. ) Below are three histograms and claims regarding the histograms. Which claim is NOT correct? ---- ( C ) (i) (ii) (iii) A) The data in chart (iii) have a larger variance than the data of chart (i) B) The data in chart (i) have a smaller mean than the data of chart (iii) C) The mode in chart (ii) is 6 D) The mean in chart (ii) is higher than. Comment [CSUSM0]: Correct because (iii) is more dispersed Comment [CSUSM]: Correct. Mean in chart (i) is, and in chart (iii) is 6 Comment [CSUSM]: Wrong. Mode is. Comment [CSUSM]: Correct. Right Skewed. Mean > Mode = Page of 7

4 Bus 0 Exam #. ( points) The data below are collected from a survey of students studying habbits. Sample size =. Answer the following questions: Surveyees Hours of study per week () ( points)organize the above raw data into a FREQUENCY table. DataValue Frequency 8 6 () ( points) Let x = the hours of study, develop a probability distribution table based on above data. (Hint, use relative frequency method to assign the probability.) x P(x) () ( points) What is the expected hours of study? (The E(x) ) E(x) = * *0. + 7*0.+8*0.+9*0.+0*0.08 = 7.68 () (8 points) Use the following table to compute the variance of x? x P(x) x-e(x) (x-e(x)) (x-e(x)) P(x) Var(x)=.776 () ( points) What is the standard deviation of x? Sqrt (.776) =.6 Page of 7

5 Bus 0 Exam #. (0 points) The following data contain the SAT scores for all the Spanishspeaking students enrolled in the ART department Spring 008. Raw Data: (the data can be downloaded from course website) a) (6 points) Create a frequency table and a relative frequency table with 6 ranges. Use reasonable upper bounds and lower bounds for each range. Max = 89 round up to 600 Min = 70 round down to 700 Range = = 900 Interval = 900/6 =0 Frequency Table 700~ ~ ~9 0~99 00~9 9 0~99 Relative Frequency Table 700~ ~ ~ ~ ~9 0. 0~ Comment [FF]: Your answer may vary due to different choice of range. However, this is the most common and straightforward choice. If your boundary contains decimals, they are not good choices. b) ( points) Create a histogram. (Draw below) 0 Draw here 700~89 80~ ~9 0~99 00~9 0~99 more c) (6 points) Calculate the quartiles: Q = 88_, Q = _0, Q=_0.7_. d) mean=079.7;median= 0; variance=69.(use varp function),range=88. Page of 7

6 Bus 0 Exam #. ( points) Systematic Sampling & Calculation Below is a list of ages for the people who have requested dental care to doctor James office. Start from the rd person in the table. Use systematic sampling technique to select of sample of 6 people. (We index people from st row starting left to right, then go to the next row) ( st ) (0 th ) ( th ) (0 th ) a) (0 points) Describe your procedure ( points) and write down your selection below ( points). The first person being picked from the sample should be no. (age ), then go by equal interval. The interval should be calculated by dividing the population size (N = 0) by the sample size ( n = 6). Therefore, the interval should be. So my next person should be the + = 8 th person, then selecting the th, 8 th, and so on. Sample Number rd 8th th 8 th th 8th Ages 8 b) ( points) What is the mean age and standard deviation of the selected sample? Mean = (++8+++)/6 = 9. STDEV=.79. Steps shown below, or use excel function stdev() x x - mean (x-mean)^ variance=sum of.67 squared distance / SD=sqrt(var).79 Page 6 of 7

7 Bus 0 Exam # 6. ( points) Probabilities and Conditional Probabilities A survey of 0 adults classified each as to gender and the number of movies attended last month. (see below table) Gender Movies attended Men Women Total or more Total What is the probability to select a person that either is a man or has not watched any movie? ( points) P(man OR no movie) = P (man) + P(no movie) P(man & no movie) = 70/0 + 60/0 0/0 = 0.7 What is the conditional probability that a person has not watched any movie given that this person is a woman? ( points) P(no movie woman) = 0/80 = 0. What is the conditional probability that a person is a man given that the person is a woman? ( points) 0 impossible. Page 7 of 7