Statistics Questions

Income Brackets The following diagram shows the movement of households in a certain country among three income groups affluent middle class and poor over the 11 year period 1980 1991 72 000 in 1994 dollars 24 000 in 1994 dollars AFFLUENT 27 9 MIDDLE CLASS 30 8 POOR 7 3 8 i a Use the transitions shown in the diagram to construct a transition matrix assuming zero probabilities for the transitions between affluent and poor Let 1 affluent 2 middle class and 3 poor 0 721 0 279 0 0 847 0 08 0 073 0 0 308 0 692 b Assuming that the trend shown was to continue what percent of households classified as affluent in 1980 were predicted to become poor in 2002 Give your answer to the nearest 0 1 22 3 04 c According to the model what percentage of all households will be in each income bracket in the long term Give your answer to the nearest 0 1 affluent 172

An introductory to psychology professor has students report their major on the first day of classes Then the professor decides to determine the major that is most representative of the students in their class Which measure of central tendency should they utilize the mean the median the mode the weighted average

A population of N 10 scores has u 21 and o 3 What is the population variance 07 100 9

What is the median for the data represented in the histogram below 4 3 f 2 1 1 80 3 N 1 2 10 X 3 4

A population of N 5 scores has a variance of o 24 If the scores were from a sample what value would be obtained for the sample variance Os 14 Os 16 Os 20

A continuous time plant is described by the state equation 1 2 H x 0 The state equation is to be solved for x t using digital computer Obtain suitable recursive relations Take sampling interval T 1 sec Show that if there is pole zero cancellation in the input output transfer function of a linea time invariant discrete time system the system will be either uncontrollable or unobservable The linear continuous time plant of a sampled data system is described by the state equation 0 1 x Determine the value of sampling period T which makes the system uncontrollable

A high school baseball conference is voting for All Area players The players names are omitted to ensure there is no favoritism when selecting the players The table below lists the top three first basemen in the conference Elimination Tool Select one answer B Hits C Player A Batting Average D A Homeruns B Which of the following is considered a categorical variable Bats Hand Runs Batted In RBIS Right Left Right Batting Average 0 325 0 315 0 298 Hits 44 42 38 Homeruns 15 10 18 Runs Batted In RBIS 58 52 60

It s family game night in Cocoa Beach Residents settle in to play their favorite game and eat their favorite snack A random sample of 115 families were asked their preferred game and snack and the results are presented in the two way table below Elimination Tool Select one answer A What proportion of Wii bowlers prefer pizza bites B C D E 12 115 23 115 12 115 Yahtzee 12 23 Trivial Pursuit Monopoly Wii Bowling Pizza Bites 10 co 14 12 Chips and Dip 3 14 7 17 7 4 Cookies 12 7

Steven is looking for a new car He knows that he is going to purchase a used car from a certain dealership To compare he decides to make a table of the three cam he intends on test driving at the dealership Elimination Tool Select one answer Car This data set contains which of the following B Ford Edge Toyota Rav 4 D Honda CRV A 6 variables 4 of which are categorical 6 variables 3 of which are categorical C 5 variables 4 of which are categorical 5 variables 3 of which are categorical Price Mileage Color 17 999 32 456 16 500 42 000 17 350 37 500 White Silver Black Drivetrain All Wheel Drive All Wheel Drive Front Wheel Drive Remote Start Yes Yes No

Jordan s starting team roster for his next fantasy basketball game is shown below His roster includes information about different variables for each of the players on his fantasy team Elimination Tool Select one answer A B C What specific variables are identified in Jordan s team roster D E Player Kev Bry Position Height and Weight Tom Player Name Position Height and Weight The 5 players Kev Bry Tom Charlie and Willy Charlie Willy The 5 different positions SF SG PG PF and C The 4 different heights and the 5 different weights 6 9 6 6 6 1 7 1 240 212 180 250 and 275 Position Height SF SG PG PF U 6 9 6 6 6 1 6 6 7 1 Weight 240 212 180 250 275

Children total 8 left handed 22 Right handed Randomly assigns 2 children to work together what is the chance they are both right handed Randomly assigns 3 Children to play a gamu what is the chance NONE of the children chosen are left hande

For the decision tree below state which decision should be made Pay attention to the minus signs The probabilities are given in brackets Decision 1 Decision 2 Decision 3 Decision 4 favourable 5 unfavourable 5 favourable 6 unfavourable 4 favourable 5 unfavourable5 favourable 5 untavourable 5 6 500 7 300 8 800 9 1000 105 400 115 600 124 1000 135 500

O Points 0 of 1 e following data represent the ages of award winners for best actor and best actress in a leading role for the 20 years from 1985 to 2004 Answer parts a b below Best Actor Ages 37 64 50 38 37 34 38 32 60 28 49 Construct an ordered back to back stem and leaf display 50 54 50 46 47 40 Best Actor Age 234 Best Actress Age 31 22 25 31 34 39 63 52 21 4140 70 45 16 points Best Actress Ages 26 26 30 39 39 31 Save Full data set 41 27

3 Assume that the readings on the thermometers are normally distributed with a mean of 0 C and a standard deviation of 1 C A thermometer is randomly selected and tested In each case draw a sketch and find the probability of each reading The given values are in Celsius degrees a Greater than 1 25 b Greater than 1 96 c Greater than 1 75 d Greater than 1 96 f Between 0 50 e Between 1 00 and 2 00 and 1 50 g Between 2 11 and 1 55 and 2 08 h Between 1 80

5 Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1 a If P 0 z a 0 3907 find a b If P b z b 0 8664 find b c If P Z c 0 0643 find c d If P z d 0 9922 find d e If P Z e 0 4500 find e f If P f z 1 59164 0 86889 find h

4 Assume that the class length of a course this summer last between 50 0 min and 58 0 min A class day is randomly selected find the probability that the class length is a Less than 51 5 min min c Between 45 5 min and 51 5 min 51 5 min and 60 6 min b Greater than 50 5 d Between

1 Inability to get along with others is the reason cited in 17 of worker firings based on data from Robert Half International Inc Concerned about her company s working conditions the personnel manager at the Boston Finance Company plans to investigate the five employee firings that occurred over the past year a Assuming that the p 17 rate applies find the probability that among those five employees n 5 the number fired because of an inability to get along with others is at least four P X 4 b If the personnel manager actually does find that at least four of the firings are due to an inability to get along with others does this company appear to be very different from other typical companies Answer YES NO Why or why not

2 Currently an average of 7 residents of the village of Westport population 760 die each year based on data from the National Center for Health Statistics a Find the mean number of deaths per day Answer b Find the probability that on a given day there are no deaths c Find the probability that on a given day there is one death d Find the probability that on a given day there is more than one death e Based on the preceding results should Westport have a contingency plan to handle Why or more than one death per day YES why not NO

Assume that human body temperatures are normally distributed with a mean of 98 21 F and a standard deviation of 0 64 F a A hospital uses 100 6 F as the lowest temperature considered to be a fever What percentage of normal and healthy persons would be considered to have a fever Does this percentage suggest that a cutoff of 100 6 F is appropriate b Physicians want to select a minimum temperature for requiring further medical tests What should that temperature be if we want only 5 0 of healthy people to exceed it Such a result is a false positive meaning that the test result is positive but the subject is r really sick Click to view page 1 of the table Click to view page 2 of the table a The percentage of normal and healthy persons considered to have a fever is 0 01 Round to two decimal places as needed Does this percentage suggest that a cutoff of 100 6 F is appropriate A No because there is a small probability that a normal and healthy person would be considered to have a fever OB No because there is a large probability that a normal and healthy person would be considered to have a fever OC Yes because there is a large probability that a normal and healthy person would be considered to have a fever D Yes because there is a small probability that a normal and healthy person would be considered to have a fever b The minimum temperature for requiring further medical tests should be F if we want only 5 0 of healthy people to exceed it Round to two decimal places as needed SXXCE

ecause the mean is very sensitive to extreme values it is not a resistant measure of center By deleting some low values and high values the trimmed mean is more esistant To find the 10 trimmed mean for a data set first arrange the data in order then delete the bottom 10 of the values and delete the top 10 of the values the calculate the mean of the remaining values Use the axial loads pounds of aluminum cans listed below for cans that are 0 0111 in thick Identify any outliers then comp the median mean 10 trimmed mean and 20 trimmed mean 246 259 268 273 277 279 280 282 285 285 287 288 290 290 294 295 296 300 311 505 The outlier s is are 505 pounds Type a whole number Use a comma to separate answers as needed B There are no outliers The median is 286 pounds Type an integer or decimal rounded to one decimal place as needed The untrimmed mean is 294 5 pounds Type an integer or decimal rounded to one decimal place as needed The 10 trimmed mean is pounds Type an integer or decimal rounded to one decimal place as needed B

Refer to the accompanying data set and use the 30 screw lengths to construct a frequency distribution Begin with a lower class limit of 0 720 in and use a class width of 0 010 in The screws were labeled as having a length of 3 4 in Click on icon to view the data Complete the frequency distribution below Frequency 3 4 11 9 0 760 0 770 3 Type integers or decimals rounded to the nearest thousandth as needed Length in 0 720 0 730 0 730 0 740 0 740 0 750 0 750 0 760 F Data table Points 0 of 2 www Screw Lengths inches 0 734 0 754 0 752 0 739 0 734 0 744 0 742 0 723 0 751 0 751 0 758 0 744 0 744 0 735 0 743 0 755 0 749 0 749 0 741 0 736 0 747 0 762 0 759 0 756 0 744 0 731 0 752 0 754 0 751 0 746 X

panying data set and use the 30 screw lengths to construct a frequency distribution Begin with a lower class limit of 0 720 in and use a class width of 0 010 in The screws were labeled as having a length of 3 4 in Click on icon to view the data Complete the frequency distribution below Frequency Length in 0 720 FIL Type integers or decimals rounded to the nearest thousandth as needed Data table CITY Screw Lengths inches 0 734 0 754 0 752 0 739 0 734 0 744 0 742 0 723 0 751 0 751 0 758 0 744 0 744 0 735 0 743 0 755 0 749 0 749 0 741 0 736 0 747 0 762 0 759 0 756 0 744 0 731 0 752 0 754 0 751 0 746 D X

The geometric mean is often used in business and economics for finding average rates of change average rates of growth or average ratios Given n values all of which are positive the geometric mean is the nth root of their product The average growth factor for money compounded at annual interest rates of 9 3 7 6 and 1 8 can be found by computing the geometric mean of 1 093 1 076 and 1 018 Find that average growth factor or geometric mean What single percentage growth rate would be the same as having three successive growth rates of 9 3 7 6 and 1 896 Is that result the same as the mean of 9 3 7 6 and 1 89 The average growth factor or geometric mean is Round to four decimal places as needed CIES

A student earned grades of B C A B and D Those courses had these corresponding numbers of credit hours 3 3 3 4 and 2 The grading system assigns quality poim to letter grades as follows A 4 B 3 C 2 D 1 F 0 Compute the grade point average GPA If the dean s list requires a GPA of 3 00 or greater did this student m the dean s list The student s GPA is Type an integer or decimal rounded to two decimal places as needed

A student s course grade is based on one midterm that counts as 10 of his final grade one class project that counts as 15 of his final grade a set of homework assignments that counts as 35 of his final grade and a final exam that counts as 40 of his final grade His midterm score is 69 his project score is 97 his homework score is 83 and his final exam score is 61 What is his overall final score What letter grade did he earn A B C D or F Assume that a mean of 90 or above is an A a mean of at least 80 but less than 90 is a B and so on His overall final score is Type an integer or a decimal Do not round Xxx

set is the magnitude of an earthquake mea on the Richter scale an outlier data value that is very far away from the others when considered in the context of the sample data given in this data set Explain Click t X d the me e mean ound to t More Info 1 99 1 26 0 45 0 96 0 63 2 45 2 13 2 12 0 35 0 98 0 19 2 66 0 58 2 19 2 08 2 74 0 37 1 52 1 55 2 45 0 77 2 72 2 18 1 88 0 25 0 35 1 16 2 15 0 14 2 51 2 97 0 41 1 58 2 86 2 96 1 61 1 51 1 15 0 07 2 83 1 31 2 31 2 33 2 04 2 34 2 74 1 84 2 72 1 51 1 52

Find the a mean b median c mode and d midrange for the data and then e answer the given question Listed below are the amounts dollars it costs for marriage proposal packages at different sports venues Are there any outliers 39 209 150 200 60 60 65 65 65 85 95 100 125 150 275 275 325 400 475 550 550 550 550 1500 2500 Type an integer or a decimal rounded to two decimal places as needed c Find the mode Select the correct choice below and if necessary fill in the answer box to complete your choice A The mode s is are 550 Type an integer or a decimal Do not round Use a comma to separate answers as needed OB There is no mode d Find the midrange The midrange is Type an integer or a decimal rounded to two decimal places as needed

The table below shows the frequency distribution of the weights in grams of pre 1964 quarters Frequency Weight g 6 000 6 049 3 6 050 6 099 6 100 6 149 6 150 6 199 6 200 6 249 6 250 6 299 6 300 6 349 6 350 6 399 4 7 10 10 4 5 1 Question 9 of 9 Use the frequency distribution to construct a histogram Does the histogram appear to depict data that have a normal distribution Why or why not Choose the correct histogram below OA OB OC Frequency Frequency Aouenbor 10 5 SOSS 20 15 104 0 6 This question 5 point s possible 6 1 6 2 6 3 Weight grams 6 1 6 1 6 2 6 3 Weight grams 6 2 Weight grams 6 3 6 4 6 4 Q Q 5 Q Q Q Q 3 Does the histogram appear to depict data that have a normal distribution OA The histogram appears to depict a normal distribution The frequencies generally increase to a maximum and then decrease and the histogram is roughly symmetric OB The histogram does not appear to depict a normal distribution The frequencies generally decrease to a minimu then increase and the histogram is roughly symmetric OC The histogram appears to depict a normal distribution The frequencies generally decrease to a minimum and the increase

A study was conducted to determine how people get jobs The table below lists data from 400 randomly selected subjects Job Sources Help wanted ads H Executive search firms E Networking N Mass mailing M 300 250 200 150 100 50 0 ENMH Frequency 23 290 66 43 O O Help wanted ads H Executive search firms E Networking N Mass mailing M Help wanted ads H Executive search firms E Networking N Mass mailing M Executive search firms E Networking N Mass mailing M Help wanted ads H Compare the pie chart found above to the Pareto chart given on the left Can you determine which graph is more effective in showing the relative importance of job sources A The Pareto chart is more effective

Use the magnitudes rounded are measured on the Richter Click the icon to view the Construct the frequency distri Magnitude Richter Freq 1 0 E Type integers or decimals D Earthquake Magnitudes Magnitudes 2 451 3 623 3 063 3 299 1 090 3 099 2 989 2 577 2 439 2 911 3 381 2 829 2 439 2 561 2 787 2 177 3 013 2 709 2 440 1 636 2 437 1 971 2 319 2 783 1 941 2 402 2 120 1 694 2 389 3 310 2 791 2 412 2 272 2 206 2 030 2 462 1 959 2 473 2 402 2 073 2 064 2 347 2 068 1 911 1 906 3 263 2 618 2 342 1 438 2 952 3 202 2 310 3 100 2 848 2 342 2 992 1 800 2 763 1 734 2 890 3 134 2 373 3 270 1 989 2 202 1 826 2 157 2 642 2 342 2 192 2 572 2 270 3 121 2 318 3 782 3 280 2 487 2 003 2 711 3 373 2 512 2 330 3 099 4 693 3 862 O X Points 0 of 1 ompanying data set to construct a frequency distribution Thi LO Does the frequency distribution appear to be a normal du

Listed below are the ages of 11 players randomly selected from the roster of a championship sports team Find the a mean b median c mode and d midrange and then e determine how the resulting statistics are fundamentally different from those calculated from the jersey numbers of the same 11 players Click the icon to view ages and jersey data and statistics a Find the mean The mean age is years Type an integer or a decimal rounded to one decimal place as needed b Find the median The median age is years Type an integer or a decimal rounded to one decimal place as needed c Find the mode Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mode s is are year s Type an integer or a decimal Do not round Use a comma to separate answers as needed OB There is no mode nominal interval Ages and Jersey Data ratio Ages 40 20 31 32 34 27 23 26 23 31 26 Jersery 7 27 47 16 14 89 73 63 60 68 61 Numbers d Find the midrange The midrange is years Type an integer or a decimal rounded to one decimal place as needed e How are the resulting statistics fundamentally different from those calculated from the jersey numbers of the same 11 players The jersey numbers are data at the level of measurement but the ages are data at the level of measurement so mean 47 7 median 60 mode none Print min 7 Done statistics are meaningful max 89 midrange 48 X

The data represents the heights of eruptions by a geyser Use the heights to construct a stemplot Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest Which plot represents a stemplot of the data O A 3 7 4 03 5 00004 6 01234 70037 802 9 0 O B 3 4 012344 7 50037 6 002 7 000 3 80 9 0 O C 3003 4 024 5 003 6 004 7 001 8 037 9 02 Height of eruption in 62 37 50 90 50 40 70 63 77 54 me 61 64 60 WANNEE 70 80 50 50 73 S 43 82 L Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest inches The values closest to the middle are inches and Type whole numbers Use ascending order

As long as the sampling method is unbiased the population parameter QUESTION 2 will und QUESTION 3 response the sampling distribution will be centered around We call the variability in our sampling distribution the standard deviation True False

Standardized IQ tests are created in such a way so that the average IQ test score is 100 and the standard deviation for an IQ score is 15 A sample of 75 individuals is taken and it is determined that their average IQ score is 110 and their standard deviation is 20 If we were to create a sampling distribution for IQ scores with a sample size of 75 what value would we expect the sampling distribution to be centered around 055 O 0 O 10 100 02 075 O 6 67

We can make a sampling distribution for any sample statistic True False QUESTION 4 True or False The standard error for the sampling distribution is equal to the standard deviation of a sample statistie True

Fill in the blank with the appropriate response As the number of sample statistics increases in a sampling distribution that is as we add more sample statistics to our sampling distribution then O the sampling distribution remains roughly the same shape as does the mean while the SE of the sampling distribution decreases O the sampling distribution becomes more unimodal and symmetric f the sample size is large enough and the mean and SE of the sampling distribution decreases while the mean stays roughly the same the sampling distribution becomes more unimodal and symmetric f the sample size is large enough the SE for the sampling distribution decreases and the mean increases the sampling distribution remains roughly the same shape as do the mean and SE of the sampling distribution the sampling distribution remains roughly the same shape while the SE of the sampling distribution decreases and the mean increases the sampling distribution becomes more unimodal and symmetric f the sample size is large enough while the mean and SE of the sampling distribution remain relatively the same

Fill in the blank with the appropriate choice As the sample size not the numbe rof sample statistics increases the sampling distribution for the sample statistic becomes wider does not change becomes narrower

he frequency distribution was obtained using a class width of 0 5 for data on cigarette tax rates Use the frequency distribution to pproximate the population mean and population standard deviation Compare these results to the actual mean u 1 557 and standard eviation o 1 067 Click the icon to view the frequency distribution for the tax rates he population mean is Round to three decimal places as needed Frequency distribution of cigarette tax rates Tax Rate 0 00 0 49 0 50 0 99 1 00 1 49 1 50 1 99 2 00 2 49 2 50 2 99 3 00 3 49 3 50 3 99 4 00 4 49 Frequency 7 13 7 6 5 4 4 1 2 X

Click the icon to view the drive through service times Construct the frequency distribution Service Time seconds Frequency 70 Type whole numbers Drive Through Service Times GEXER 120 116 131 147 120 126 136 77 136 121 146 138 110 149 148 110 79 120 91 159 83 199 198 137 142 76 259 192 106 153 151 109 102 78 166 195 253 145 171 160 133 105 224 231 124 X

Identity which of these types of sampling is used random systematic convenience stratified or cluster A large company wants to administer a satisfaction survey to its current customers Using their customer database the company randomly selects 50 customers and asks them about their level of satisfaction with the company What type of sampling is used O Systematic O Stratified O Convenience O Cluster Random

An investment counselor calls with a hot stock tip He believes that if the economy remains strong the investment will result in a profit of 50 000 If the economy grows at a moderate pace the investment will result in a profit of 10 000 However if the economy goes into recession the investment will result in a loss of 50 000 You contact an economist who believes there is a 20 probability the economy will remain strong a 70 probability the economy will grow at a moderate pace and a 10 probability the economy will slip int recession What is the expected profit from this investment The expected profit is Type an integer or a decimal

Male and female populations of humpback whales under 80 years old are represented by age in the table below Complete parts a through d Age 0 9 10 19 20 29 30 39 40 49 50 59 60 69 70 79 Males 9 13 18 15 25 23 17 12 Females 6 8 13 18 21 21 16 12 a Approximate the population mean and standard deviation of age for males 42 50 years Round to two decimal places as needed o 20 20 years Round to two decimal places as needed b Approximate the population mean and standard deviation of age for females years Round to two decimal places as needed

What are the null and alternative hypotheses OA Ho 3 50 H p 3 50 A data set includes data from student evaluations of courses The summary statistics are n 98 x 3 35 s 0 55 Use a 0 05 significance level to test the claim that the population of student course evaluations has a mean equal to 3 50 Assume that a simple random sam been selected Identify the null and alternative hypotheses test statistic P value and state the final conclusion that addresses the original claim OC Ho H 3 50 H 3 50 Determine the test statistic Round to two decimal places as needed J B Ho H 350 H 3 50 Points 0 33 of 2 OD H H 3 50 H 3 50 13 8 67 30 points S

The frequency distribution was obtained using a class width of 0 5 for data on cigarette tax rates Use the frequency distribution to approximate the population mean and population standard deviation Compare these results to the actual mean 1 557 and standa deviation o 1 067 Click the icon to view the frequency distribution for the tax rates The population mean is Round to three decimal plac

Patty has just completed her second semester in college She earned a grade of A in her 1 hour linear algebra course a grade of C in her 1 hour economics course a grade of D in her 5 hour enginee course and a grade of A in her 4 hour creative writing course Assuming that A equals 4 points B equals 3 points C equals 2 points D equals 1 point and F is worth no points determine Patty s grad average for the semester Patty s grade point average is Round to two decimal places as needed

According to a study 81 of K 12 schools or districts in a country use digital content such as ebooks audio books and digital textbooks Of these 81 6 out of 10 use digital content as part of their curriculum Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum

According to records the amount of precipitation in a certain city on a November day has a mean of 0 10 inches with a standard deviation of 0 07 inches What is the probability that the mean daily precipitation will be 0 098 inches or more for a random sample of 40 November days taken over many years Carry your intermediate computations to at least four decimal places Round your answer to at least three decima places

Ullen frequency distributions are reported using unequal class widths because the frequencies of some groups would otherwise be small or very large Consider the following data which represent the daytime household temperature the thermostat is set to when someone is home for a random sample of 728 households Determine the class midpoint if necessary for each class and approximate the m and standard deviation temperature Click the icon to view the frequency distribution for the daytime household temperature Class 61 64 65 67 68 69 70 71 72 Class Midpoint 73 76 77 80 Round to one decimal place as needed SCLER Frequency distribution Temperature F 61 64 65 67 68 69 70 71 72 73 76 77 80 Print Frequency 32 61 190 190 117 84 54 Done X

Karl and Leonard want to make confetti In order to get the right balance of ingredients for their tastes they bought 5 pounds of paper hearts at 4 33 per pound 2 pounds of sparkling stars for 3 59 p pound and 2 pounds of shiny coils for 3 89 per pound Determine the cost per pound of the confetti The cost per pound of the confetti is Round to the nearest cent C

Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more Jo JE JE decimal places Round your Send data to Excel Observed frequency fo Expected frequency JE Jo JE JE Part 2 Winter 23 40 00 7 225 Spring 38 40 00 responses to three or more decimal places 0 100 Summer 54 40 00 4 900 a Determine the type of test statistic to use Type of test statistic Chi square Fall 45 40 00 0 625 Total 160 Answer the following to summarize the test of the hypothesis that birthdays are equally likely during each season of the year Use the 0 10 level of significance for the test Degrees of freedom 6 X b Find the value of the test statistic Round your answer to two or more decimal places 12 85 c Find the critical value Round your answer to two or more decimal places 10 64 d Can we reject the hypothesis that birthdays are equally likely during each season of the year BEET