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1 Math 227 Winter 2017 Practice Test 1 (Ch1-Ch4) Name Provide an appropriate response. 1) Define the terms population, sample, parameter and statistic. Identify the sample and population. Also, determine whether the sample is likely to be representative of the population. 2) An employee at the local ice cream parlor asks three customers if they like chocolate ice cream. Provide an appropriate response. 3) Define random sample. Explain why this is important in design of experiments. 4) An education expert is researching teaching methods and wishes to interview teachers from a particular school district. She randomly selects ten schools from the district and interviews all of the teachers at the selected schools. Does this sampling plan result in a random sample? Simple random sample? Explain. A) Yes; no. The sample is random because all teachers have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample that includes teachers from schools that were not selected. B) No; yes. The sample is not random because teachers in small schools are more likely to be selected than teachers in larger schools. It is a simple random sample because all samples have the same chance of being selected. C) Yes; yes. The sample is random because all teachers have the same chance of being selected. It is a simple random sample because all samples have the same chance of being selected. D) No; no. The sample is not random because teachers in small schools are more likely to be selected than teachers in larger schools. It is not a simple random sample because some samples are not possible, such as a sample that includes teachers from schools that were not selected. 5) A psychology student wishes to investigate differences in political opinions between business majors and political science majors at her college. She randomly selects 100 students from the 260 business majors and 100 students from the 180 political science majors. Does this sampling plan result in a random sample? Simple random sample? Explain. A) Yes; yes. The sample is random because all students have the same chance of being selected. It is a simple random sample because all samples of size 200 have the same chance of being selected. B) No; no. The sample is not random because political science majors have a greater chance of being selected than business majors. It is not a simple random sample because some samples are not possible, such as a sample consisting of 50 business majors and 150 political science majors. C) No; yes. The sample is not random because political science majors have a greater chance of being selected than business majors. It is a simple random sample because all samples of size 200 have the same chance of being selected. D) Yes; no. The sample is random because all students have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample consisting of 50 business majors and 150 political science majors. 1

2 6) In a survey, 26 voters were asked their ages. The results are shown below. Construct a histogram to represent the data (with 5 classes beginning with a lower class limit of 19.5 and a class width of 10). What is the approximate age at the center? Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. 7) Listed below are the amounts of weight change (in pounds) for 12 women during their first year of work after graduating from college. Positive values correspond to women who gained weight and negative values correspond to women who lost weight. What is the mean weight change? Find the mode(s) for the given sample data. 8) The weights (in ounces) of 14 different apples are shown below Find the mean and median for each of the two samples, then compare the two sets of results. 9) The Body Mass Index (BMI) is measured for a random sample of men from two different colleges. Interpret the results by determining whether there is a difference between the two data sets that is not apparent from a comparison of the measures of center. If there is, what is it? Baxter College Banter College Find the mean of the data summarized in the given frequency distribution. 10) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the mean waiting time. Round your answer to one decimal place. Waiting time (minutes) Number of customers

3 Solve the problem. 11) A student earned grades of C, A, B, and A. Those courses had these corresponding numbers of credit hours: 3, 6, 2, and 6. The grading system assigns quality points to letter grades as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Compute the grade point average (GPA) and round the result to two decimal places. Find the range for the given sample data. 12) Listed below are the amounts of weight change (in pounds) for ten women during their first year of work after graduating from college. Positive values correspond to women who gained weight and negative values correspond to women who lost weight. What is the range? Find the variance for the given data. Round your answer to one more decimal place than the original data. 13) Jeanne is currently taking college zoology. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores: Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. 14) The top nine scores on the organic chemistry midterm are as follows. 47, 55, 71, 41, 82, 57, 25, 66, 81 Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results. 15) When investigating times required for drive-through service, the following results (in seconds) were obtained. Restaurant A Restaurant B Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. 16) The maximum value of a distribution is 40.8 and the minimum value is 2.4. Use the empirical rule to solve the problem. 17) At one college, GPA's are normally distributed with a mean of 3 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.4 and 3.6? Find the indicated probability. 18) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 3? Answer the question. 19) In a certain town, 10% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle? Answer the question, considering an event to be "unusual" if its probability is less than or equal to ) Assume that a study of 500 randomly selected school bus routes showed that 482 arrived on time. Is it "unusual" for a school bus to arrive late? Find the indicated probability. 21) A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 7 wood and 14 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective. 3

4 22) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a face card or a 4). 23) A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if necessary. 24) A sample of 4 different calculators is randomly selected from a group containing 47 that are defective and 29 that have no defects. What is the probability that all four of the calculators selected are defective? Round to four decimal places. 25) The table below describes the smoking habits of a group of asthma sufferers. Light Heavy Nonsmoker smoker smoker Total Men Women Total If two different people are randomly selected from the 954 subjects, find the probability that they are both women. Round to four decimal places. Find the indicated probability. Round to the nearest thousandth. 26) A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 40 that have no defects. What is the probability that at least one of the calculators is defective? Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. 27) The following table contains data from a study of two airlines which fly to Small Town, USA. Number of flights Number of flights which were on time which were late Podunk Airlines 33 6 Upstate Airlines 43 5 If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight which was on time. 4

5 Answer Key Testname: MATH227_WINTER PRETEST 1 1) A population is the complete collection of all elements. A sample is a subset of elements drawn from a population. A parameter is a numerical measurement describing some characteristic of a population. A statistic is a numerical measurement describing some characteristic of a sample. A census is the collection of data from every element in a population; a sample is a subset of a population. 2) Sample: the 3 selected customers; population: all customers; not representative 3) In random sampling, each member of the population has an equal chance of being selected. Random sampling provides us with the best representative sample in which all groups of the population are approximately proportionately represented. Careless sampling can easily result in a biased sample which may be useless. 4) A 5) B 6) The approximate age at the center is 50. 7) 2.8 lb 8) 5.0 oz, 6.2 oz 9) Baxter College: mean = 24; median = 24 Banter College: mean = 24.25; median = 24.5 Even though the measures of center are roughly the same, the Banter College values are much more varied than the Baxter College values. 10) 9.3 min 11) ) 35 lb 13) ) ) Restaurant A: 57 sec; sec 2 ; sec Restaurant B: 77 sec; sec 2 ; sec There is more variation in the times for restaurant B. 16) ) 68% 1 18) 18 19) 9 : 1 20) Yes 21) ) 13 23) ) ) )

6 Answer Key Testname: MATH227_WINTER PRETEST 1 27)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Ch 2 Test Remediation Work Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) High temperatures in a certain