MATH112 STATISTICS; REVIEW1 CH1,2,&3 Name___________________________________ CH1 Vocabulary 1) A statistics student wants to find some information about all college students who ride a bike. She collected data from other students in her class who ride a bike to school. The following table shows data about their bikes: Color Black Blue Green Black Series Number Weight (lbs) A120 32 B640 20 C300 29 D90 15 Road Bike 0 1 0 1 Average Speed (mph) 16 24 14 23 a) How many variables are there? b) What is the sample size? c) What is the population? d) Which variables are quantitative? e) Which variables are qualitative? 2) The average gas mileage of the top selling mini-vans for each U. S. car manufacturer is an example of what type of variable? 3) Marital status of each member of a randomly selected group of adults is an example of what type of variable? 4) Give an example of one categorical variable and one numerical variable. Indicate whether the study described is an observational study or a controlled experiment. WHY? 5) The obesity rates of elementary age children living in urban areas are compared to those living in rural areas to see whether children in urban settings have higher obesity rates. 6) A group of students is divided into two groups. One group is a given a new chewable vitamin and the other group is given a placebo. After six months they are asked to fill out a questionnaire and given a health exam to see whether the new vitamin has health benefits that are better than a placebo. Proportions and Percentages. 7) A recent report showed there were 48 accidents involving pedestrians in City A and 62 accidents involving pedestrians in City B this year. The mayor of City A claims that his city is safer for pedestrians than City B. What information is missing that might contradict this claim? In a study of 900 adults, 45 out of the 325 men in the study said that they preferred to rent a movie on DVD rather than going out to a movie theater. 8) What is the approximate percentage of men in this study who prefer to rent a movie on DVD? 9) What is the approximate percentage of women who participated in this study? 1 The two-way table below shows the survey results when sixty adults were asked whether they had made a clothing purchase in the last thirty days. 10) What percentage of the sample had not made a clothing purchase in the past thirty days? 11) Of the adult males surveyed, what percentage had made a clothing purchase in the last thirty days? Correlation. 12) Consider the following statement: "Researchers conducted a large observational study and determined that children who participated in school music programs scored higher on math exams in later grades than those who did not." Suppose that upon hearing this a politician states that all children should participate in school music programs. What is wrong with the politician's statement? A group of 500 patients who suffer from skin cancer were asked to participate in a study to determine the effectiveness of a new medication. The patients were randomly divided into two groups, one that was given the actual medication, and one that received a placebo pill. A good outcome was defined as the cancer being in remission after 6 months of treatment. The results of the study are below. 13) Approximately what percent of patients who took the medication had cancer remission? 14) Was the new medication effective for cancer remission? 15) Can we conclude that the cancer remissions were caused by the new medication? 2 CH2 A fitness instructor measured the heart rates of the participants in a yoga class at the conclusion of the class. The data is summarized in the histogram below. There were fifteen people who participated in the class between the ages of 25 and 45. Use the histogram to answer the question. 16) How many participants had a heart rate between 120 and 130 bpm? 17) How many participants had a heart rate between 140 and 150 bpm? 18) What percentage of the participants had a heart rate greater than 130 bpm? 19) What is the approximate percentage of participants that had a heart rate less than 130 bpm? 20) Each day for twenty days a record store owner counts the number of customers who purchase an album by a certain artist. The data and a dotplot of the data are shown below: Data set: 1, 3, 4, 4, 5, 6, 7, 2, 3, 4, 4, 5, 6, 8, 2, 3, 4, 5, 6, 7, 9 Explain some key features of the disytribution. For example Which is the shape? Where is the bulk (center) of the data? Does the data have allot of variation,WHY? are there any outliers? Construct the dotplot for the given data. 21) The following data represent the number of cars passing through a toll booth during a certain time period over a number of days. 28 29 27 27 34 28 31 28 29 25 32 29 33 27 31 25 30 35 3 22) The following histogram represents audience movie ratings (on a scale of 1-100) of 489 movies. What is the typical movie rating given by audiences according to this distribution? 23) What is the typical value for the histogram shown below? 24) The histogram shows the distribution of pitch speeds for a sample of 75 pitches for a college pitcher during one season. Describes the distribution of the histogram below. Shape? Center? 4 25) The histogram below is the distribution of heights for a randomly selected Boy Scout troupe. Describes the distribution of the histogram below. Shape? Center? Be able to describe some distributions. Choose the histogram that matches the description. 26) The distribution of heights of adult males tends to be symmetrical with no outliers. A) This distribution is roughly symmetrical and appears to resemble a normal distribution B) This distribution is skewed to the right with no outliers C) This distribution is skewed to the left with what appears to be some outliers 5 27) Order the following histograms from least to most variability. . 28) The bar charts below depict the marital statuses of Americans, separated by gender. Which bar chart shows more variability in marital status? Why? Construct a pie chart representing the given data set. 29) The following data give the distribution of the types of houses in a town containing 22,000 houses. House Type Frequency Percentage Cape 5500 25% Garrison 8800 35% Split 7700 40% 6 The following double-bar graph illustrates the revenue for a company for the four quarters of the year for two different years. Use the graph to answer the question. 30) In what quarter was the revenue the greatest for Year 1? 31) In what quarter was the revenue the least for Year 2? 32) What was the revenue for the third quarter of Year 1? 7 CH3 Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place than that used for the observations. 33) Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age. 57 64 64 55 65 58 68 54 55 34) For the pair of histograms below, determine which distribution has the larger standard deviation. Solve the problem. 35) A class of 20 history students took a quiz worth 100 points. The standard deviation of the scores was 0. What can you say about the scores of the students on this quiz? Use the empirical rule to solve the problem. 36) At one college, GPA's have a distribution that is unimodal and symmetric with a mean of 2.9 and a standard deviation of 0.4 a) What is the range of GPA's from one standard deviation below the mean to one standard deviation above the mean? b) Between what two values would you expect to find 95% of GPA's 37) The mean price of a pound of ground beef in 75 cities in the Midwest is $2.11 and the standard deviation is $0.56. A histogram of the data shows that the distribution is symmetrical. A local Midwest grocer is selling a pound of ground beef for $3.25. What is this price in standard units? Assuming the Empirical Rule applies, would this price be unusual or not? Round to the nearest hundredth. Provide an appropriate response. 38) A television station claims that the amount of advertising per hour of broadcast time has an average of 14 minutes and a standard deviation equal to 2.6 minutes. You watch the station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 11 minutes. Calculate the z-score for this amount of advertising time. Is it unusual? 8 Use the following information to answer the question. The distribution of the number of hours of sleep people get per night is unimodal and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours. 39) If James had a z-score of 1.2, explain what this value means in terms of the number of hours of sleep he gets. Find the median for the given sample data. 40) The salaries of ten randomly selected doctors are shown below. $109,000 $109,000 $173,000 $219,000 $241,000 $100,000 $140,000 $808,000 $235,000 $156,000 Determine the interquartile range. 41) Determine the interquartile range. 2, 3, 5, 8, 9, 12, 2, 3, 5, 8, 9, 12 Provide an appropriate response. 42) The annual profits of five large corporations in a certain area are given below. Find the mean and median. Which measure of central tendency should be used? why? $134,000 $142,000 $162,000 $132,000 $1,212,000 Provide an appropriate response. 43) Here are the heights in inches of the male and female employees at First City Bank. Compare the interquartile ranges of the heights of male and female employees. Male 62 64 66 66 68 70 73 75 78 Female 56 59 60 62 66 66 68 71 73 9 44) The boxplots below represent movie runtimes (length of a movie in minutes) for movies that have been rated by the Motion Picture Association of America as R, PG-13, PG, and G. List ratings according to their median runtimes, from shortest to longest. Solve the problem. 45) Calculate the five-number summary for the following dataset. and make a boxplot. 51 53 62 34 36 39 43 63 73 79 . 46) Ten parents were asked the ages of their youngest child. The results are shown below. 6 25 12 20 6 2 17 22 23 10 What is the IQR for this set of data? 10 Answer Key Testname: STAT_CCC_REV1 1) a) 5 b) 4 c) All college students who ride bikes d) weight & speed e) color, series # and road bike 2) Numerical variable 3) Categorical variable 4) Answers will vary. Examples might include: categorical - gender, favorite candy, year in school, favorite color, etc.; numerical - age, height, weight, speed, etc. 5) Observational study, since there is no munipulation of any group 6) Controlled experiment, since we are munipulating one of the groups. 7) The total number of pedestrians in both City A and City B 8) 13.8% 9) 63.9% 10) 35% 11) 50% 12) The politician confused correlation with causation. "Correlation does not imply causation" 13) 67% 14) Yes, a higher percent of patients who took the medication had cancer remissions than the patients who took the placebo. 15) Yes, this is a controlled experiment. Since a higher percent of patients who took the medication had cancer remissions, we can conclude causation. 16) 3 17) 2 18) 53% 19) 47% 20) The dotplot shows that this data has a roughly bell-shaped distribution. The center is around 4, Not allot of variation since most values occur between 3 and 6 over the 20 day spread. no outliers. 21) 25 30 35 22) The typical value is about 60. 23) Since the data are bimodal, there are two typical values - one is about 20 and the other is about 60. 24) The distribution is symmetricc with a mean pitch speed around 93 mph. 25) Skewed left with an outlier. with a median height of about 4 ft. 26) A 27) (iii), (i), (ii) 28) The female bar chart shows more variability because there are more observations in the different categories than there are for males. 29) 30) fourth quarter 31) second quarter 32) $35 million 11 Answer Key Testname: STAT_CCC_REV1 33) 60 yr 34) (i) has a larger standard deviation than (ii). 35) Every student received the same score on the quiz. 36) a) 2.5 to 3.3 b) 2.1 to 3.7 37) z = 2.04; This is unusually expensive ground beef. 38) z = -1.15: No since it is within two standard deviations 39) The number of hours James sleeps is 1.2 standard deviations above the mean. 40) $164,500 41) 6 42) $356,400: $142,000; median since there is an outlier 43) Male: 9 Female: 10 44) G, PG, R, PG-13 45) 34, 39, 52, 63, 79 46) When the values are arranged in order (2, 6, 6, 10, 12, 17, 20, 22, 23, 25), we find that Q3 = 22 and Q1 = 6. Therefore, IQR = Q3 - Q1 = 22 - 6 = 16. 12