# Statistics Questions

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Statistics

ProbabilitySolve by substitution or elimination by subtraction or addition 4x 15y 17 4x 20y 52

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Probabilitystem of inequalities linear inequalities 8 6 B C 4 A 7z 14y 0 8 6 0 61 8 2 is graphed Which region below represents the solution to the system of 4 D 6 M 8

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StatisticsThe box plot shows the heights of grade 7 students in two random samples from two different schools The sample item from each school is 30 of the student population School A School B B Heights of Grade 7 Students 4 Based on the box plot which comparison is true Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in the interquartile ranges of grade 7 student heights at the schools D 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 Height inches Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in t medians of grade 7 student heights at the schools Grade 7 students from School A are typically taller than grade 7 students from School B because of the difference in th interquartile ranges of grade 7 student heights at the schools Grade 7 students from School A are typically taller than grade 7 students from School B because of the difference in medians of grade 7 student heights at the schools

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Statistics27 Which choice shows a set of data that could be represented by the box plot shown below 0 5 10 A 1 3 5 6 6 8 13 14 19 20 B 1 2 3 5 7 8 8 13 19 20 1 5 5 6 6 6 8 13 19 20 13567 7 8 13 10 20 15 20

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Probability1 A drawer contains 3 black socks 6 white socks 1 green sock and 10 blue socks Determine the probability of randomly selecting a sock that is not green

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StatisticsThe dot plot shows the Each dot represents 1 country 7 8 B 18 1 14 19 23 9 What is the mean number of public holidays A 20 17 10 15 11 12 13 Number of Public Holidays 17 18 16 14

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Statistics7 The dot plot shows the number of public Each dot represents 1 country 7 8 B 18 1 c 14 19 9 What is the mean number of public holidays A 20 17 D 23 10 11 12 13 14 Number of Public Holidays 15 16 DO 17 18

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StatisticsCorinne is planning a beach vacation in July and is analyzing the daily high temperatures for her potential destination She would like to choose a destination with a high median temperature and a small interquartile range She constructed box plots shown in the diagram below Ocean Beach Serene Shores Whispering Palms 70 75 80 85 90 95 100 70 75 80 85 90 95 100 Which destination has a median temperature above 80 degrees and the smallest interquartile range A Pelican Beach B Ocean Beach D Whispering Palms Pelican Beach Serene Shores

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Statisticsline plots below to compare the quiz scores for her first period math class and her second period math class She gave the same quiz to each class B QUIZ SCORES First Period Class X X X X X X AHH 0 1 2 3 4 5 6 7 8 9 10 Points X X Second Period Class X X X X X X X X X X X X X X 0 1 2 3 X X 4 5 6 Points 7 8 9 10 What conclusion can Ms Andrews make about the performance of her first and second period classes A The second period class scores had a higher mean than the first period class scores The first period class had a higher median score than the second period class

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StatisticsB The students in a study group each measured the thickness of their math notebooks The results are shown in the lineplot below A 1 inches 8 1 B 2 inches 2 2 8 7 C 2 inches 8 3 8 Thickness of Notebook inches 3 D 2 inches 8 4 8 If the students stack their notebooks one on top the other what will be the total thickness of the stack 5 8 68

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ProbabilityA B D 9 Amounts of Trall Mix 15 2 XXXXX 1 4 How much total trail mix in cups did Elijah eat 15 4 Xx Cup xx 3 4

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ProbabilityThere is a spinner with 18 equal areas number 1 18 If the spinner is spun one time what is the probability that the result is a multiple of 2 or a multiple of 5 P multiple of 2 or multiple of 5

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Statistics20 The principal of the school is looking over grade reports specifically scores on math quizzes This box and whisker plot shows the results Find median and range in the given box plot Math quiz scores 50 Median 60 70 80 and Range 90

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ProbabilityA bag contains flavored lollipops A lollipop will be randomly selected from the bag 17 lollipops are grape flavored 8 lollipops are cherry flavored 14 lollipops are watermelon flavored 16 lollipops are strawberry flavored What is the probability in decimal form that the selected lollipop will be either cherry flavored or watermelon flavored

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Statistics5 The test scores of the students in Mr Duffy s class are shown on the line plot below MR DUFFY S CLASS x XX XXX X X X X x X X X X X A 60 65 70 75 80 85 90 95 100 Most of the students in Ms Guzman s class scored higher than most of the students in Mr Duffy s class on the same test Which line plot could represent the test scores of the students in Ms Guzman s class MS GUZMAN S CLASS A x x B X X X X 4 1 X X X 60 65 70 75 80 85 90 95 100 MS GUZMAN S CLASS X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 60 65 70 75 80 85 90 95 100

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StatisticsBOX PLOT The box and whisker plot describes the number of absences for Mr Fitz s students F 4 6 8 10 12 14 According to the plot what percent of the students were absent between 4 and 6 days A 100 B 50 25 D 75

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StatisticsUse the box plot below to fill in the blanks to the five number summary below Cost of each lunch for the month in dollars H 4 5 Minimum Maximum Median First Quartile Third Quartile 6 7 8 H 9 10

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Statistics3 12 points Graph the function y 22 Find z and y intercepts hor izontal and vertical asymptotes all critical numbers intervals of in de creasing local absolute max min x 1 Draw your graph on the next page

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StatisticsBelow is a hypothesis test set up by a student who recently took introductory statistics Ho x 5 HA X 5 The sample mean of 100 cases used to implement the hypothesis test is x 4 2 Which of the following statements are accurate i This is a one sided hypothesis test ii There is an error in how these hypotheses were constructed iii It would be reasonable to swap for z in the alternative hypothesis Oi only O ii only iii only Oi and ii Oi and iii O ii and iii

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StatisticsLess than 55 of Internet users pay bills online Express the null and alternative hypotheses in symbolia form for this claim enter as a percentage Ho P H P Use the following codes to enter the following symbols

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StatisticsA New York Times article titled For Runners Soft Ground Can Be Hard on the Body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury One position supported running on soft surfaces to relieve joints that were in recovery from injury The second position supported running on hard surfaces since soft surfaces can be uneven which may make worse those injuries a soft surface was intended to help Suppose we are given sufficient funds to run an experiment to study this topic With no studies to support either position which of the following hypotheses would be appropriate O The first position is more sensible so this should be a one sided test In this case we should form the alternative hypothesis around the second position O The second position makes the more sense so this should be a one sided test In this case we should form the alternative hypothesis around the first position O Because we would be interested in any difference between running on hard and soft surfaces we should use a two sided hypothesis test O Because there is uncertainty we should postpone defining the hypotheses until after we collect data to guide the test

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ProbabilityThe national average SAT score is roughly 1500 We would like to see if the high school seniors who apply to Duke have higher than average SAT scores We randomly sample 100 applicants files and record their SAT scores Which of the following is the correct set of hypotheses for this research question Hint think about how many samples we have data from O Ho x 1500 HA 1500 O Ho H 1500 HA H 1500 O Ho P 1500 HA P 1500 O Ho H 1500 HA H 1500 Ho H Duke H National HA H Duke National

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ProbabilityMore than 18 of people support legalizing gay marriage Express the null and alternative hypotheses in symbolic form for this claim enter as a percentage Ho P H p Use the following codes to enter the following symbols enter

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StatisticsA commonly cited standard for one way length duration of school bus rides for elementary school children is 30 minutes A local government office in a rural area randomly samples 100 elementary school children in their district and find an average one way commute time of 38 minutes with a standard deviation of 8 minutes Which of the following is the correct set of hypotheses for testing if the average commute time of elementary school students in this district is different than the commonly cited standard of 30 minutes O Ho H 30 HA x 38 O Ho x 38 HA H 30 O Ho H 30 HA 30 OHA H 30 Ho x 30 Ho H 30 HA 30

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ProbabilityThe mean weight of male nurses working at a local hospital is more than 174 lbs Express the null and alternative hypotheses in symbolic form for this claim Ho p H p Use the following codes to enter the following symbols enter

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StatisticsTo evaluate the effectiveness review sessions a professor gave a pre test before the review and a post test after The results are shown in the table below 50 REE 19 Pre test 1 Post test 22 7 0 49 60 79 37 67 57 60 61 65 92 16 35 13 Difference d x 1 22 57 22 33 25 63 4 24 47 10 X0 23 37 78 17 43 22 0 38 20 1 The null and alternative hypotheses would be Ho Pa H Ha o o OF o o 58 Can we say that the review session significantly harms test performance at 10 significance level 8 8 5 8 o

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Statisticspost test after The results are shown in the table below Pre test 1 Post test 48 58 46 55 65 55 60 60 46 59 42 63 42 69 Difference d 22 21 68 11 60 16 62 3 17 76 21 13 9 8 14 Can we say that the review session makes a significant difference on test performance at 5 significance level 1 The null and alternative hypotheses would be Ho Ha Select an answer H Ha Select an answer 2 The tail type of the test is Select an answer 3 The sample statistic d is

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StatisticsSolve the equation for the variable Write your solution as a simplified root If there are 2 solutions list them with a comma separating them Example 27 27 or 3 5 3 5 If there is no solution enter DNE 4x 8 392 X

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ProbabilityUse the quadratic formula to solve the equation Be sure to simplify your answers Enter both answers separated by a comma 4x 64 0

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Statisticsolve the absolute value equation or indicate that the equation has no solution with x 2 7

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ProbabilitySolve the equation 6x 10 3 algebraically If your answer is a fraction write it in reduced fraction form Do NOT convert the answer to a decimal X

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StatisticsYou spin the spinner once 3 2 What is P divisor of 42 Simplify your answer and write it as a fraction or whole number

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Statistics3 If the population deviation o is known and we wish to estimate the population mean u with 95 confidence what is the appropriate critical value z to use a 1 28 b 1 645 c 1 96 d 2 33 The lower limit of a confidence interval at the 95 level of confidence for the population proportion when the sample size of 100 had 30 successes is a 0 3898 b 0 2102 d 0 3041 4 0 2959 1

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Probability6 A box contains 4 red and 3 green ornaments TWO ornaments are randomly selected without replacement Find the indicated probabilities A What is the probability both ornaments are red B What is the probability that the 1st one is red and the 2nd one is green C What is the probability both ornaments are the same color

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ProbabilityE 5 A store offers a special Christmas purchase in which for a fixed cost you can choose from 1 of two pants 1 of four shirts and 1 of five ties How many different outfits are available

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StatisticsComplete parts a through d for the sampling distribution of the sample mean shown in the accompanying graph Click the icon to view the graph a What is the value of The value of is 300 b What is the value of o The value of o is 40 c If the sample size is n 16 what is likely true about the shape of the population OA The shape of the population is skewed left B The shape of the population is approximately normal OC The shape of the population is skewed right OD The shape of the population cannot be determined d If the sample size is n 16 what is the standard deviation of the population from which the sample was drawn The standard deviation of the population from which the sample was drawn is

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Statisticspost test after The results are shown in the table below Pre test 1 59 57 66 44 73 64 59 72 51 Post test 2 65 31 56 48 18 36 8 67 36 63 4 Difference d x2 1 28 0 o 0 2 The tail type of the test is Left Tailed 3 The sample statistic d is 1 44 7 28 7 1 The null and alternative hypotheses would be Ho Pa H Pd 6 q o B q OF Can we say that the review session significantly harms test performance at 5 significance level E OF E B B

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StatisticsSeveral years ago 47 of parents who had children in grades K 12 were satisfied with the quality of education the students receive A recent poll asked 1 105 parents who have children in grades K 12 if they were satisfied with the quality of education the students receive Of the 1 105 surveyed 468 indicated that they were satisfied Construct a 95 confidence interval to assess whether this represents evidence that parents attitudes toward the quality of education have changed What are the null and alternative hypotheses Ho P versus H p Type integers or decimals rounded to two decimal places as needed Use technology to find the 95 confidence interval We are 95 confident the proportion of parents who had children in grades K 12 that were satisfied with the quality of education the students receive is between and Type integers or decimals rounded to two decimal places as needed What is the correct conclusion O A Since the interval does not contain the proportion stated in the null hypothesis there is insufficient evidence that parents attitudes toward the quality of education have changed OB Since the interval contains the proportion stated in the null hypothesis there is sufficient evidence that parents attitudes toward the quality of education have changed OC Since the interval contains the proportion stated in the null hypothesis there is insufficient evidence that parents attitudes toward the quality of education have changed O D Since the interval does not contain the proportion stated in the null hypothesis there is sufficient evidence that parents attitudes toward the quality of education have changed

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StatisticsAs part of a survey 17 college graduates and 18 non graduates were asked How many hours did you spend at your job last week The results are shown in the stem and leaf display below Answer the questions that follow Number of hours at work Graduates Non graduates 996 223678 87730 312468 9974310 40003778 32 53 Key 26 6 2 2 22 a What were the ranges for the two groups 0 0 Graduates Non graduates b Which group had the higher median number of hours O Graduates O Non graduates O The medians were the same c Which group had more responses in the 50s O Graduates O Non graduates Fach X 5

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StatisticsA certain drug can be used to reduce the acid produced by the body and heal damage to the esophagus due to acid reflux The manufacturer of the drug claims that more than 91 of patients taking the drug are healed within 8 weeks In clinical trials 206 of 223 patients suffering from acid reflux disease were healed after 8 weeks Test the manufacturer s claim at the x 0 05 level of significance Because npo 1 Po Round to one decimal place as needed What are the null and alternative hypotheses 10 the sample size is Ho versus H Type integers or decimals Do not round Find the test statistic Zo Zo Round to two decimal places as needed Find the P value P value Choose the correct conclusion below 5 of the population size and the sample the requirements for testing the hypothesis satisfied Round to three decimal places as needed O A Reject the null hypothesis There is insufficient evidence to conclude that more than 91 of patients taking the drug are healed within 8 weeks OB Reject the null hypothesis There is sufficient evidence to conclude that more than 91 of patients taking the drug are healed within 8 weeks OC Do not reject the null hypothesis There is insufficient evidence to conclude that more than 91 of patients taking the drug are healed within 8 weeks O D Do not reject the null hypothesis There is sufficient evidence to conclude more than 91 of patients taking the drug are healed within 8 weeks

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Statistics19 Which of the following is a negative side effect of using macroeconomic policies to offset a recessionary gap A crowding out of private investment B possibly unpredictable consequences of the stabilizing macroeconomic policies a higher aggregate price level C D all of the answer choices provided are negative side effect of using macroeconomic policies