Statistics Questions and Answers

Shawna finds a study of American women that had an equation to predict weight in pounds from height in inches y 260 6 6x Shawna s height was 64 inches and her weight was 150 pounds What is the value of the residual for Shawna s weight and height O 730 pounds O 12 4 pounds O 12 4 pounds O 162 4 pounds

The table below shows the grade and reading level for 5 students Student 1 O 0 71 Student 2 O 0 85 Student 3 O 1 00 Student 4 Student 5 1 x X 7 Sx Grade 2 Sy 6 For grade the mean is 3 6 and the standard deviation is 2 1 For reading level the mean is 9 2 and the standard deviation is 4 1 5 4 1 Reading Level 6 Using the formula below or Excel find the correlation coefficient r for this set of students Answer choices are rounded to the nearest hundredth 14 12 10 4

Which of the following statements is TRUE O High correlation always implies causation O High correlation does not always imply causation O Only a correlation of 1 implies causation O Only a correlation of O implies causation

The scatterplot below shows the relationship between the grams of fat and total calories in different food items Grams of Fat vs Total Calories Total Calories O 549 54 O 417 56 700 525 350 175 O 0 10 20 Grams of Fat The equation for the least squares regression line to this data set is 13 198x 153 6 What is the predicted number of total calories for a food item that contains 25 grams of fat 30 40

For a math assignment Michelle rolls a set of three standard dice at the same time and notes the results of each trial What is the total number of outcomes for each trial O 18 O 36 O 216 O 27

Tracie spins the four colored spinner shown below She records the total number of times the spinner lands on the color red and constructs a graph to visualize her results Which of the following statements is TRUE

The midterm exam scores obtained by boys and girls in a class are listed in the table below Midterm Scores Boys 9 78 6689 44789 0012 355567 112 36889 12 0004 Key 1612 means 62 points Stem 0 1 2 3 4 5 6 7 8 9 What does the circled section represent O Eight boys scored 12 points on the exam OTwelve boys scored 8 points on the exam O Eight boys scored over 10 points on the exam Girls 56 775 3345 8864 000056 98123 77756 456 11

Which of the following statements about a negatively skewed distribution is true O The distribution of the data features two modes O The mean and median have the same value O The distribution of the data tails to the right of the median The distribution of the data tails to the left of the median

Select the statement that is FALSE O The interquartile range is always equal to or smaller than the range O The range is never greater than the greatest value of a data set O The mean is never greater than the greatest value of a data set O The range is the difference between the largest and smallest values of a data set

In which of these cases should the median be used O When the data has small variance O When data has no outliers O When the data has extreme values O When the data has nominal values

Frequency O 16 68 15 18 10 5 O 1 5 8 00 6 10 15 11 15 7 16 20 The relative cumulative frequency of students who earned a score of 21 or higher on the quiz is 7 21 25 Grade on Quiz 3 26 30 31 35 2 36 40

40 O 40 The first quartile Q1 value from the above box plot is O 54 O 47 47 O 65 54 65

Which of the following statements about a normal distribution is true The normal distribution is an example of a bimodal distribution OA large portion of the data is skewed to the right OA large portion of the data is located near the tails O The normal distribution is single peaked and symmetric

1 Lumber companies dry freshly cut boards in kilns 1 Lumber companies dry freshly cut boards in kilns before selling them As a result of the drying process a certain percentage of the boards crack The current drying procedure is known to produce cracks in 16 of the boards The drying supervisor wants to test a new method to determine if fewer boards will crack a State appropriate hypotheses for a significance test in this setting To investigate he selected an SRS of 50 boards dried them using the new method and found 5 that cracked p 5 50 0 10 To determine if these data provide convincing evidence that less than 16 of the boards will crack when using the new method 100 trials of a simulation were conducted Each dot in the graph below shows the proportion of boards that cracked in a random sample of 50 boards assuming that each board has a 16 chance of cracking b Use the simulation results to estimate the P value of the test c Interpret the P value d What conclusion would you make using a 0 05

Question 9 For a class reading competition the students were asked to read a book Mike Jack and Rayon discussed the numbers of pages they read on the first day One of them made a graph to represent the data Number of Pages Read on First Day Number of Pages Read 80 75 70 65 60 55 50 Jack Who made the graph and why Rayon Name OM because he wanted to accurately show the amount read by each person Mike O Mk because he wanted to make the amount read by each person appear reasonably close je because he wanted to make it look like he read significantly more than the others

1 2 5 points Thirty five engineering students are randomly selected in a study to determine the number of hours outside of the class that students study in a week The data obtained is summarized as Average 34 75 Median 35 25 Lower fourth 28 85 Upper fourth 39 25 The two lowest data points are 12 and 13 and the two largest data points are 49 and 53 a 1 5 points Determine the outliers mild or extreme in the weekly study hours if there are any b 1 point All the students are registered in a computer lab that holds 1 5 hours every week If this time is added as study time for each student What will be the new mean study time of the selected students

2 4 3 points A study involves determining the average waiting time minutes when a customer requests Uber service from UB 16 randomly selected waiting times are provided below 16 2 7 13 21 38 24 18 22 42 26 23 20 23 a 1 5 points Calculate the 10 trimmed average waiting time using the data provided 17 b 1 5 points Compare and interpret the standard deviation of the data used to obtain the 10 trimmed mean and the standard deviation of the original data

Mike s electronics store sold the following number of cellphones on each of the seven days of a week Sunday Monday Tuesday Wednesday Thursday Friday Saturday O 5 phones O 9 phones O 70 phones Day 10 phones 12 10 9 5 14 The mean number of cell phones sold by the store for the week was 10 10 Cell Phones Sold

The formula for the standard deviation of a sample is S 1 11 n 1 1 X X Select the true statement for the following data set that has a mean of 9 3 7 8 8 8 9 10 10 13 14 Answer choices are rounded to the hundredths place O O The variance is 8 50 and the standard deviation is 3 09 The variance is 9 56 and the standard deviation is 8 50 The variance is 3 09 and the standard deviation is 9 56 The variance is 9 56 and the standard deviation is 3 09

percent Factors in Load OA O C 100 OB 90 80 70 60 50 Jul Passenger Load Factor on all U S Scheduled Airlines A Aug Sep Oct B Nov Dec Jan Months Which segment of the graph indicates no change in the passenger load C Feb D Mar Apr E May Jun

The dot plot below shows the height in cm of students in a class 130 O 10 O 12 How many students are taller than 140 centimeters 08 135 11 140 Height in centimeters 145 150

Question 1 his chart shows the number of students of different age groups who participated in a quiz Number of Students Average Age of Students Participating in Quiz Competition 120 100 80 60 40 20 0 15 16 Which of the following statements about the stack plot is true 17 18 Age There were more male students than female students in the age group 19 20 There were more male students in the age group 19 20 than in the age group 15 16 There were more students in the age group 15 16 than in any other age group 19 20 Girls Boys

In a survey to rate the pizzas served by a pizza parlor 250 people rated their agreement with the statement The pizzas here are one of the best I ve ever had The answers were put into a table Strongly Agree Agree Neutral Disagree Strongly Disagree O 20 O 27 O 10 8 Rating 17 6 27 50 75 The relative frequency of people who strongly agree with the statement is 54 44 Frequency

3 Mark Z is interested in finding out if there is an association between age group and Facebook use among U S adults He takes a random sample of 250 U S adults aged 18 or older and records their age and whether or not they use Facebook The two way table summarizes the results 22 Facebook user Yes Total orin till sinohale 191 60 going2 rato3 8 9 59 Total 68 68 30 250 demon Do the data provide convincing evidence of an association between age group and whether or not someone uses Facebook for all U S adults No 18 29 1422 ESOP axez 30 49 64 Age years 20 84 50 64 46 22 ar PE BE 65 ST 2 21 loorb lood52 gi sllvisso sol aizviens nolien prerupe toast who go goo bee adgang woul toxpran bu tentang asb

2 Do high school students in Michigan and California have the same music preferences We used the Census at School website to select separate random samples of 100 high school students from Michigan and 100 high school students from California Students were asked What is your favorite music genre The two way table summarizes their responses State Favorite music genre California Michigan Country 12 Pop 15 Rap 21 Rock 7 10 Other 45 50 Total 100 100 200 Do these data provide convincing evidence at the a 0 05 level that the distributions of favorite music genre differ for high school students in Michigan and California 4 14 22 gobiva 82 Total 16 29 43 40 17 95 rodinu

A new pet food product for small dogs has been developed to help with tooth decay Fifty two dogs participate in the study Each dog owner picks a card from a standard deck out of a hat If the card is red their dog will be in the treatment group If the card is black their dog will be in the placebo group Which experimental design was used O Randomized Block Design O Case Control Design O Completely Randomized Design

1 Nathan wondered if the different types of animals used for anim equal proportions He took a random sample of 686 animal crackers and got the distribution of animals shown in the table Do these data provide convincing evidence that the type of animal used for animal crackers is not uniformly distributed 1107 Animal Number Animal Number 31 es Cow ze 005 40 Polar Bear Horse B64 Donkey 51 SOM 58 Buffalo 42 02 Moose 52 21 Cat tail Cat no tail ts 48book for 56 Elephant 60 Lion anders adul 55 001 Camel Ca 61 Wombat 55 doo Goat 44 to znobudhizib ar tard level 20 0 s is sonsbivsgnisalvos abivorq stab sead Simplifs bas me irbi ni ztrebude loodbe daid tot 10 laums str

A factory manufactures bolts One of its employees working in the quality control department checks the first 20 bolts manufactured in a day for possible defects This is what type of sampling O Systematic sampling Voluntary response sampling O Convenience sampling O Stratified sampling

Jenae changed the original coffee labels with plain white ones that had the flavor printed in bold black letters and she placed them on the coffee pots for the week long experiment Jenae used an aspect of experimental design known as labels to have the same appearance O randomization O a treatment O a control O replication when she created the

A local gym conducts a survey among the people in a mall Which survey question would have a qualitative response O How much do you weigh in pounds O How many servings of fruits do you eat every day What is the amount of weight you can bench press in pounds O Do you exercise daily

The following shows the Consumer Price Index CPI for the years 2000 2005 All of the values use a reference year of 1983 Consumer Price Index 2000 2005 195 190 185 180 175 170 165 172 4 2000 178 2001 179 9 2002 O 100 in 2000 would be equivalent to 189 7 in 2004 O 100 in 1983 would be equivalent to 189 70 in 2004 Which of the following is true about the CPI based on the information O 100 in 2002 would be equivalent to 189 70 in 2004 Year O 100 in 2004 would have been worth 189 70 in 1983 183 7 2003 189 7 2004 194 5 2005

An appliance store manager noted that the sales of home appliances contributed 74 of the store s profits in the year 2010 and 82 in the year 2011 Of the following choices which statement about home appliance sales is true O Home appliance sales increased profits by 9 75 O Home appliance sales increased profits by 8 O Home appliance sales increased profits by 8 percentage points Home appliance sales increased profits by 9 75 percentage points

Select the correct statement regarding experiments O A researcher can carefully control the explanatory variables but not observe human responses A researcher can carefully control the explanatory variables and observe human O responses O A researcher can ignore explanatory variables and observe human responses A researcher can observe the explanatory variables but not control human responses

A research team conducts a survey to determine the area of land used for farming in lowa The team randomly selects house addresses and sends the survey by mail Which type of sampling method is the research team using O Systematic random sampling O Simple random sampling O Cluster sampling O Multi stage sampling

A hunter is practicing his aim using a practice target He takes 5 shots All 5 shots hit the target but they do not hit or surround the bullseye In addition all 5 shots are very spread apart on the target Classify the hunter s accuracy and precision O Low accuracy and low precision High accuracy and low precision O High accuracy and high precision Low accuracy and high precision

Researchers want to test the effects of a new weight loss program They believe that gender is a significant factor The participants are divided by gender Then within each group participants are randomly assigned to either the treatment or control group Which of the following would be the most effective to test the effects of the new weight loss program O A matched pair design experiment O O A randomized block design experiment A longitudinal observational study A completely randomized design experiment

James conducts a survey to study the relationship between cell phone use and grades earned during the fall semester James suspects that there might be a lot of other factors that affect grades besides cell phones Which of the following could be a confounding variable in James s study Time spent studying O Time spent using a cell phone O Grade earned during the spring semester O Grade earned during the fall semester

Jenae is able to purchase a different brand of coffee for half the price from a new supplier She anticipated that her co workers would object to switching to the new brand as they were really partial to the coffee they have been drinking so far Indeed when offered a taste test of the old brand versus the new brand her co workers unanimously rejected the new brand Jenae s boss Steven pointed out that this result was most likely due to the fact that the taste test was not O blinded O randomized O replicated O controlled

Which of the following data types will be continuous O Number of people in a family O Height of a toddler O Number of chairs in a house O Cost of a can of tuna fish

Scientists want to test a new pair of running shoes A speed test is performed with two separate groups of participants The treatment group will wear the new pair of running shoes while the control group will not It is believed that age and height may affect speed Which of the following would be most effective in controlling the confounding variables such as age and height in this study O A matched pair design experiment O A completely randomized design experiment O A retrospective observational study OA longitudinal observational study

Rob sent an email survey to 2 000 cell phone owners asking about their satisfaction with their current plan Only 256 people returned the survey and they were predominately 18 24 years old Which of the following statements is true O Rob is ignoring the assumption that all survey participants will want to act independently O The survey suffers from census issues because only 256 people responded O The survey likely has bias because the people who could not answer differ from those who did answer O Rob included too many people on the survey list affecting the data collected

Nick designs a clinical trial to test a new anxiety medication by creating a control group and a treatment group If he gives the medication to patients in the treatment group and not to the control group some patients might find out that they re not being treated To improve his study Nick decides to give a sugar pill to the control group The sugar pill is an example of a O case control O placebo O confounding variable variable of interest

Of 400 randomly selected people in the city of Lyon France 60 people had the first name Hugo Which of these does NOT represent inferential statistics 15 of the people who live in Lyon have the first name Hugo 15 of the people who live in France have the first name Hugo O 15 of the people who live in Europe have the first name Hugo 15 of the people surveyed have the first name Hugo

In a bolt manufacturing factory it is estimated that 6 of the bolts being manufactured will be defective with a 3 margin of error Choose the statement that correctly describes the confidence interval The percentage of defective bolts is between 3 and 6 The percentage of defective bolts is 6 or more O The percentage of defective bolts is 6 or less O The percentage of defective bolts is between 3 and 9

The owner of a pizza parlor called every fifth person who ordered pizza last week to rate the pizza What type of statistical study is this O An experiment O An observational study O A census O A survey

An insurance firm wants to estimate the percentage of senior citizens in a small town with approximately 2 534 residents It asks a group of 85 randomly selected people in the town about their age Select the statement that is TRUE O The sample is 85 people The population is 2 449 people O None of the answer choices are true O The sample is 85 people The population is 2 534 people The sample is 2 534 people The population is 85 people

A local school newspaper s editor wants to survey students to determine the approval rating of the current student council president How would the newspaper apply the cluster sampling method to find this information O The newspaper staff surveys every student in the lunchroom and science room O The newspaper staff surveys only the female students in the entire school O The newspaper staff surveys random students from every grade in the school O The newspaper staff surveys every student in a randomly selected grade

Melissa is conducting a survey of her classmates because her teacher wants the class to learn more about hygiene habits Melissa has developed a list of 10 questions Do you brush your teeth every day is the first question she asks Which type of question is Melissa asking O Open question O Closed and binomial question O Closed question Open and binomial question

5 A random sample of 10 students was selected from the senior class at each of four large high schools and the score of each of these 40 students on a certain mathematics ex amination was observed Suppose that for the 10 students from each school the sample mean and the sample vari ance of the scores were as shown in Table 11 18 Test the hypothesis that the senior classes at all four high schools would perform equally well on this examination Discuss carefully the assumptions that you are making in carrying out this test Table 11 18 Data for Exercise 5 School 1 2 3 4 Sample mean Sample variance 105 7 102 0 93 5 110 8 30 3 54 4 25 0 36 4

23 In this problem we discuss the global truncation error associated with the Euler method for the initial value problem y f t y y to yo Assuming that the functions f and Jy are continuous in a closed bounded region R of the ty plane that includes the point toyo it can be shown that there exists a constant L such that if t y f t Lly l where t y and 1 are any two points in R with the same t coordinate see Problem 15 of Section 2 8 Further we assume that f is continuous so the solution has a continuous second derivative a Using Eq 20 show that En En hflt tn f n Yn h o a Enl Bh where a 1 hL and max 1 1 1 2 on to tn b Accepting without proof that if E 0 and if E satisfies Eq i then En Bh a 1 a 1 for a 1 show that El ii Equation ii gives a bound for E in terms of h L n and B Notice that for a fixed t this error bound increases with increasing n that is the error bound increases with distance from the starting point fo c Show that 1 hL e hence En sal enkl 1 hL 1 L Bh e 10 1 L i Bh For a fixed point T to nh that is nh is constant and h T to n this error bound is of the form of a constant times h and approaches zero as h 0 Also note that for nhL T to L small the right side of the preceding equation is approximately 12a T