Statistics Questions and Answers

Defects Answer O 09 6 S 3 Cl T 6 Hours of Training Step 2 of 2 Describe the relationship indicated by the scatterplot and the correlation coefficient from Step 1 0 Land 2 3 4 DO Loosely clustered in a negative linear fashion O No linear relationship Tightly clustered in a negative linear fashion O Loosely clustered in a positive linear fashion Tightly clustered in a positive linear fashion 10

A manufacturing company which produces laminate for countertops is interested in studying the relationship between the number of hours of training an employee receives and the number of defects per countertop produced Ten employees are randomly selected The number of hours of training which each employee has received is recorded and the number of defects on the most recent countertop produced is determined The results are as follows Defects Hours of Training 5 9 4 7 I 9 60 C a 16 3 O Employee Training 7 6 7 3 2 Defects per Countertop Copy Data 0 6 1 8 2 4 3 5 6 Hours of Training 7 Enable Zoom Pan Defects per Countertop

Defects Ch 0 4 9 10 w CL O 4 3 6 Copy Data Pest 15111 6 Hours of Training 30 Determine the correlation coefficient Round your answer to two decimal places I 6 Defects per Countertop 3 I Enable Zoom Pan 18 9 10

Describe the relationship indicated by Answer

A crew of Astronauts mined a nearby asteroid that contains precious metals The miners where able to extract 4345 30200 lbs of cobalt from I eight of the asteroid They project that the remainder of the asteroid proportionally contains the same amount of cobalt every eighth contains 4345 30200 lbs of cobalt If the price of Cobalt is 0 03418 per gram How much do the Astronauts expect to make from their Expedition Use the same procedure from above using steps a b c 1 0 lb equals 453 5924g

group of five individuals with high blood pressure were given a new drug that was designed to lowe lood pressure Systolic blood pressure was measured before and after treatment for each individual Th esults follow Construct a 95 confidence interval for the mean reduction in systolic blood pressure Before After 1 170 145 2 164 132 Individual 3 168 129 4 158 135 5 183 145

in group 2 The sample statistics are in the below table Group 1 16 20 Sample Size Sample Mean Sample Standard deviation Question 8 The degrees of freedom are 6 44 Solve the following questions 8 10 O 3 707 4 O 1 943 Group 2 9 14 1 960 3 Researchers want to construct a 95 confidence interval for the difference in means from the two locations What percentile would you use to construct the confidence interval 1 pts

Suppose you flip a coin 100 times and get 55 heads Construct a 95 confidence interval for p the true probability that the coin lands heads O 0 0649 1 O 0 468 0 632 O 0422 0 678 O 0452 0 648 O 0401 0 699

Trail Let rattlesnakes from Blue Ridge Trail be in group 1 and rattlesnakes from Homestead Trail be in group 2 The sample statistics are in the below table Sample Size Sample Mean Sample Standard deviation Question 10 Group 1 16 20 4 Yes The degrees of freedom are 6 44 Solve the following questions 8 10 Group 2 9 14 3 Is the Blue Ridge Trail more dangerous than the Homestead Trail based on the CI The larger number of rattlesnakes means the more dangerous O Not enough information to determine it 1 pts

A random sample of 300 shoppers at a large supermarket includes 234 who regularly use discount coupons Construct a 98 confidence interval for the probability that any one shopper at that supermarket randomly chosen for an interview will confirm that he or she regularly uses discount coupons Does your confidence interval support that the majority of people will regularly use discount coupons p 0 5 Not enough information to determine it O No Yes

sample standard deviation was 13 8 Solve the following questions 1 5 Question 1 What is the standard error of the sample mean O 0 276 O 1 952 O 56 3 O 3 81 1 pts

Student government members survey every 15th student who enters the school building and asks whether students favor the school s new school mascot The sample statistics show that 57 oppose the new school mascot 37 favor the new school mascot and 6 have no opinion Use this information to answers parts a through c What is the population Select What is the sample Select What general conclusion can be made about the population Select Select A plurality of students favor the new school mascot A minority of students oppose the new school mascot A majority of students have no opinion of the new school mascot A majority of students oppose the new school mascot 1 pt

For a class project a student studies the likelihood that students turn in their homework each day For each of her classes she observes the teacher collect homework She records the number of students who turn in homework and the number who do not The resulting data show that 72 of students turned in homework on time and 13 of students did not turn in any homework at all during the week Use this information to answer parts a through c What type of sampling method was used Select What type of study was performed Select Can the student use these statistics to make a general conclusion about all students in her school Select Select Yes the sample size and number of school days are large enough to represent all students in he No the students in her classes know she is observing them Yor the students in her classes represent all students in her school

Identify the type of study method described in the following situation and explain whether the sample statistics can be used to make a general conclusion about the population A list of students is randomly generated from the school database Information for every student is entered into the database and each student has an equally likely chance of being selected The students selected are asked how much time they spend on household chores each week Choose the correct answer below Observational study the statistics are somewhat unreliable in this study because not all students have an equally likely chance of being selected Although the data collected cannot be used to make a general conclusion about the entire population it may still be useful information O Controlled experiment the statistics of this study can be used to make a general conclusion about the time spent on household chores for these particular students as compared with other students not in the study O Survey the statistics can be used to make a general conclusion about the population because the samel is randomly generated and the survey question does not introduce a bias into the study

Student government members survey every 5th student who enters the school building and asks whether students favor the school s new school mascot The sample statistics show that 52 favor the new school mascot 42 oppose the new school mascot and 6 have no opinion Use this information to answers parts a through c What is the population Select What is the sample Select What general conclusion can be made about the population Select Select A majority of students favor the new school mascot A majority of students have no opinion of the new school mascot A plurality of students oppose the new school mascot A minority of students favor the new school mascot 1

Determine if the following is quantitative or categorical Favorite baseball team O Quantitative O None O Categorical

g disease in peach tree seedlings might be controlled with weed and soil treatment An experiment was conducted to compare peach tree seedling growth with soil and weeds treated with one of two herbicides In a field containing 20 seedlings 10 were randomly selected from throughout the field and assigned to receive Herbicide A The remaining 10 seedlings were to receive Herbicide B Soil and weeds for each seedling were treated with the appropriate herbicide and at the end of the study period the height in centimeters was recorded for each seedling A box plot of each data set showed no indication of non Normality The following results were obtained Herbicide A Herbicide B Select one A 95 confidence interval for HB HA is given by which of the following expressions Use the conservative value for degrees of freedom a b C d e x cm 94 5 109 1 109 1 94 5 1 96 109 194 5 2 262 109 1 94 5 10 10 109 1 94 5 1 96 109 1 94 5 2 262 10 9 9 10 9 9 10 10 92 10 10 10 10 s cm 10 9 10

Ips claims that his secret sleep tapes cause people to become better at basic algebra All you have to do the doctor explains is listen to my tapes while you sleep at night and you ll be better at algebra in two months A math teacher at a local high school has expressed interest but demands evidence Five students from this school are randomly selected They take an algebra skills test listen to Dr Visegrips tape for two months while they sleep and then take a second test The test scores are given here Student Pretest Posttest elect one a b C Which of the following is the correct 99 confidence interval for the true mean difference posttest pretest in scores d e 1 48 1 2 4 604 5 70 6 69 4 3 250 1 48 1 2 4 604 4 1 2 2 576 1 48 1 2 2 576 76 143 Test scores A 68 70 2 972 3 362 5 5 B 69 68 C 74 75 D 71 72 E 65 68

Twenty five seniors from a large metropolitan area school district volunteer to allow their Math SAT test scores to be used in a study These twenty five seniors had a mean Math SAT score of x 450 with a standard deviation of s 100 Assuming that the population of Math SAT scores for seniors in the district is approximately normally distributed which of the following gives the correct 90 confidence interval for u Select one a 450 4 b The confidence interval cannot be determined because the conditions for this inference procedure have not been met C 450 100 d 450 20 e 450 34 2

An advertising firm is comparing two different 30 second television ads for a new mobile phone A group of 48 volunteers is divided randomly into two groups of 24 and each group watches one of the ads Afterwards all the subjects are asked to estimate on a scale of 1 no way to 10 definitely whether they would consider buying this phone the next time they upgrade to a new phone Let and 2 represent the mean rating we would observe for the entire population represented by the volunteers if all members of this population saw the first or second ad respectively The data is given in the table below Dot plots for the two sets of ratings show no indication of non Normality Ad 1 Ad 2 n e 24 24 Which of the following is a correct interpretation of this interval X 6 1 4 8 S 1 7 1 3 Select one a We are 98 confident that this interval captures the true difference in mean rating for the first and second ad b 98 of the intervals construction this way will contain the value 0 C There is a 98 probability that we have not captured the true difference in the population means d There is a 0 98 probability that the true difference in mean rating for the first and second ad in this interval 98 of the time the true difference in mean rating between the first and second ad will be in this interval

A study of the impact of caffeine consumption on reaction time was designed to correct for the impact of subjects prior sleep deprivation by dividing the 24 subjects into 12 pairs on the basis of the average hours of sleep they had had for the previous 5 nights That is the two with the highest average sleep were a pair then the two with the next highest average sleep etc One randomly selected member of each pair was allowed to drink two cups of caffeinated coffee and the other drank two cups of decaf Each subject s performance on a standard reaction time test was recorded Which of the following is the correct check of the Normal Large Sample condition for this significance test Select one a Confirm graphically that the scores of the caffeine drinkers and the scores of the decaf drinks in the study and the differences in scores within each pair of subjects could have come from Normal distributions b Confirm that at least one of the sets of individual scores from the caffeine or decaf group and the differences in scores within each pair could have come from Normal distributions c Confirm that the differences in scores within each pair of subjects could have come from a Normal distribution d Because the central limit theorem applies to this situation it is not necessary to check any of the samples for Normality e Confirm graphically that the scores of the caffeine drinkers and the scores of the decaf drinks in the study could have come from Normal distributions A O 10 SP E n ED 150 DA h Sock E PANAS

A researcher studying reaction time of drivers states that A 95 confidence interval for the mean time it takes for a driver to apply the brakes after seeing the brake lights on a vehicle in front of him is 1 2 to 1 8 seconds Which of the following claims is justified Select one a A reporter claims that any randomly selected driver will take at least 1 2 seconds to apply the brakes after seeing the brake lights on a vehicle in front of him b A reporter claims that the mean amount of time it takes to apply the brakes after seeing the brake lights on a vehicle in front of him is at least 1 2 seconds c A reporter claims that it takes at least 1 5 seconds to apply the brakes after seeing the brake lights on a vehicle in front of him reporter claims that it takes at least 2 seconds to apply the brakes after seeing the brake lights on a vehicle in front of him e A reporter claims that it takes 1 2 or 1 8 seconds to apply the brakes after seeing the brake lights on a vehicle in front of him d

Below are dot plots from five different samples Which sample does not satisfy the Large sample Normal condition for performing one sample t procedures Sample sizes A n 34 B n 32 C n 27 D n 10 E n 12 A B D E 0 Select one T 3 B a Sample C b Sample D Sample E c d Sample B e Sample A 6 T 9 12 15 18 T 21

Does listening to music increase the speed at which people complete routine tasks Fifteen volunteers are asked to sort 100 red and white beads into two piles according to color once while listening to Handel s Water Music and once in silence the order music or silence first is determined for each subject by the flip of a coin Here are the data along with summary statistics in the last two columns Subject Handel Silence Difference Select one a b C d 1 e 14 16 2 2 15 18 3 0 4 2 145 0 4 1 96 0 4 1 96 3 4 5 6 17 21 13 18 17 20 15 17 0 1 2 1 0 4 2 145 1 96 15 1 96 15 19 0 18 6 2 145 1 96 14 1 96 14 7 21 22 8 24 27 1 3 5 04 5 13 15 15 9 15 14 1 We want to estimate the mean difference Silence Handel in time to sort the beads with and without music Which of the following is the appropriate 95 confidence interval T 887 10 25 22 20 32 3 2 2620 12 30 3212 15 14 15 Y 16 H 7 15 HH BEL 13 17 1 S 18 6 5 04 19 0 5 13 1 96 0 4 E

There are many ways to measure the reading ability of children Research designed to improve reading performance is dependent on good measures of the outcome One frequently used test is the DRP or Degree of Reading Power A researcher suspects that the mean score u of all third graders in Henrico County Schools is different from the national mean which is 32 To test her suspicion she administers the DRP to an SRS of 28 Henrico County third grade students The mean DRP score for this group of students is 35 09 with a standard deviation of 11 19 An inspection of the data shows no skewness or serious departures from normality a Construct a 90 confidence interval for the mean DRP score for all Henrico County third graders b Use the confidence interval you constructed in a to comment on whether you agree with the researcher s claim Explain your reasoning clearly

Twenty onion seeds were randomly assigned in pairs to two different types of soil Soil A and Soil B The first pair of seeds were planted nearest to a window and received plenty of sunlight The next two seeds were planted in each type of soil and were placed 6 inches away from the window The third pair of seeds were planted in each type of soil and were placed 1 foot away from the window and so on After 6 months the onions were harvested and their diameters were measured in centimeters The dotplot below shows the mean difference Soil A Soil B in diameter for each pair of onion seeds 2 2 1 5 1 0 5 0 0 5 1 1 5 Difference Soil A Soil B in diameter cm Select one Which of the following accurately describes what the dotplot reveals about whether Soil A tends to produce larger onions than soil B O a It does not appear that Soil A tends to produce larger onions than Soil B because the sample size is too small O b It does not appear that Soil A tends to produce larger onions than Soil B because the distribution of differences is skewed fairly symmetric O e O c It does not appear that Soil A tends to produce larger onions than Soil B because 5 of the differences are positive O d It does not appear that Soil A tends to produce larger onio than Soil B because only 5 of the differences are positive It does not appear that Soil A tends to produce larger onions than Soil B because 1 of the difform

What is the critical value t for a 99 confidence interval when n 20 Select one O a 2 845 O b 2 093 O c 2 861 O d 2 576 O e 2 086

assistant takes a random sample of 15 mothers with at least two children from the hospital records and records the birthweights of the first two children in pounds Birth Weight of next older sibling Birth Weight of younger sibling Difference 5 1 5 3 6 7 4 7 3 8 5 8 8 3 6 4 6 1 6 4 5 8 7 8 5 3 4 5 6 6 Select one 1 3 0 5 1 1 0 6 0 7 Which of the following is the correct value and interpretation of the standard deviation of the differences younger sibling next older sibling a 1 24 and 1 46 The standard deviation of the weights of the younger sibling tends to be 1 24 pounds and the standard deviation of the weights of the next older sibling tends to be 1 46 pounds on average b 0 893 The weight of the younger sibling tends to be 0 893 pounds less on average than their next older sibling O c 0 483 The mean difference younger sibling next older sibling in birth weight tends to vary on average 0 483 pounds from a mean difference of zero pounds d 0 483 The weight of the younger sibling tends to be 0 483 pounds greater on average than their next older sibling e 0 483 The mean difference 0 8 9 5 7 8 5 4 9 3 2 5 6 6 4 5 9 5 6 4 1 2 0 6 2 4 0 7 0 8 6 1 7 3 6 6 0 5 0 9 0 7

The heights in inches of females in the United States are believed to be Normally distributed with mean The average height of a random sample of twenty five American adult females is found to be x 64 5 inches and the standard deviation of the twenty five heights is found to be s 4 15 What is the value of the standard error of x Select one O a 0 83 O b 0 65 O c 1 96 O d 0 15 O e 4 15

Pauly s Pizza claims that the mean time it takes for them to deliver a pizza to dorms at Nate s college is 30 minutes After a long wait one night Nate decides to test this claim He randomly selects 15 dormitory residents and asks them to record the time it takes for Pauly s Pizza to deliver the next time they order pizza Here are the results in minutes 31 38 39 25 26 454232 2338 42 21 40 37 28 a The sample mean is x 33 8 and the sample standard deviation is sx 7 72 Calculate and interpret the standard error of the mean for these data b Construct and interpret a 90 confidence interval for the true mean delivery time Does the data support

The manager of a fast food restaurant wants to estimate the true mean order to delivery time for all customers during the noon to 1 pm lunch hour From a random sample of 40 orders the manager calculated a 95 confidence interval to be 4 6 minutes to 8 8 minutes a What is the point estimate from this sample b What is the margin of error c Interpret the confidence interval d Interpret the confidence level

Find the critical t value for each of the following confidence intervals a 95 confidence interval with 10 degrees of freedom b 70 confidence interval when n 24

A travel agent is interested in the average price of a and determines the price of a regular room with a k prices are normally distributed Construct an interva confidence Round the endpoints to two decimal pla

A survey asks What beverage do you drink in the morning and offers choices Tea only Coffee only Both coffee and tea Neither coffee nor tea The results are presented in the following Venn Diagram Tea Coffee 32 31 48 15 How many people drink only coffee in the morning How many people drink coffee in the morning How many people do not drink coffee How many people were surveyed people people people people

Cars in a parking lot SUV 13 5 9 3 Red 6 Honda 5 7 How many SUV s are in the parking lot 6 How many red Hondas are in the parking lot How many cars are in the parking lot a How many of the red cars in the parking lot are not SUV s

A 11 C 3 n AUB n Ant n An BnC n AUBUC n AOBOG 2 8 4 1 Determine the following cardinalities n A 7 B 5

Write a quadratic regression equation for the following data rounding all coefficients to the nearest hundredth 8 8 9 16 10 12 15 19 21 Y 315 396 461 583 686 693 621

ice Simulation this experiment we throw two dice repeatedly and compute the relative frequency that the outcome is a double We saw above that the probability is 1 6 1667 Press any of t Throw Dice buttons in succession to see the graph of relative frequency versus the number of throws N As N gets large the relative frequency should approach the modeled robability of 1 6 Throw Dice Throw Dice 10x N Sample size 0 fr E Frequency 0 04 0 3 02 0 1 Throw Dice 100x Throw Dice 1000x Reset Difference Red Green 0 PE relative frequency

4 8 po The Boston Security Analyst Society Inc BSAS is a nonprofit association that serves as a forum for the exchange of ideas for the investment community Suppose the ages of its members are based on the following frequency distribution Age Frequency Midpoint m m fi From 18 to 25 From 25 to 35 From 35 to 45 From 45 to 55 From 55 to 65 From 60 to 90 5 14 42 29 23 17 m x fi note fill in the table correctly and completely to receive full credit a Use the summarized data to find out the average age of members 2nd decimal place b What is the sample variance and standard deviation of member s age 2nd decimal

An FDA representative randomly selects 12 packages of ground chuck from a fat contents have an approximately normal distribution The resulting measu 13 15 15 Anquer 18 19 13 Step 1 of 2 Calculate the sample mean and the sample standard deviation

An FDA representative randomly selects 8 packages of ground chuck fat contents have an approximately normal distribution The resultin 14 15 Step 1 of 2 Calculate the sample mean and the sample standard d

The weights in pounds of 20 diabetes patients are given 177 184 188 191 197 202 208 208 215 217 218 221 221 226 231 234 240 319 333 340 Find the mean and 15 trimmed mean

Suppose the preliteracy scores of three year old students in the United States are normally distributed Shelia a preschool teacher wants to estimate the mean score on preliteracy tests for the population of three year olds She draws a simple random sample of 20 students from her class of three year olds and records their preliteracy scores in points 81 84 87 91 91 91 92 92 94 95 97 99 100 102 106 107 107 111 115 116 Click to download the data in your preferred format CrunchIt CSV Excel JMP Mac Texty Minitab14 18 Minitab18 PC Text R SPSS TI Calc I Calculate the sample mean x sample standard deviation s and standard error SE of the students scores Round your answers to four decimal places

of estion What are the mean variance nearest tenth 1 9 4 12 13 13 a mean 10 5 variance 2 2

A tower that is 102 feet tall casts a shadow 132 feet long Find the angle of elevation of the sun to the nearest degree 0 132 ft T 102 ft

7 Write the augm

DETERMINE THE ORDER OF A MATRIX Determine the order of the matrices A 1 4 3 1 3 0 2 3 Determine the value of the given element 191 B

A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels Cholesterol evels in milligrams per deciliter were measured before and after treatment for each individual with the following results Individual Before 1 296 2 289 3 280 4 295 5 281 6 281 7 283 8 285 Send data to Excel Part 0 2 Part 1 of 2 After 218 214 180 205 168 201 170 182 a Use a calculator to construct a 90 confidence interval for the mean reduction in cholesterol level Round your answers to at least one decimal place

Complete the following task The following are the scores from a statistics test Step 1 Organize the following data set of 25 with a stem and leaf in order to see the frequency of each test score 85 64 27 69 86 95 97 64 65 82 36 85 95 97 86 85 95 90 91 78 75 78 75 85 96 Step 2 Create a frequency distribution table for the data with 8 classes Create a table with class intervals frequency relative frequency cumulative frequency and cumulative relative frequency for the given data Step 3 Analyze your results Write a small summary of your findings include which class had the highest frequency and which had the lowest and the assumptions you would make based on this data The summary must be 5 6 sentences long to earn full credit

Next Save Pause LLARD FRANCHETTE Kenneth surveyed 1000 people about the change in the balance of their bank accounts over the course of a week He recorded his data and calculated a mean and a median Then he realized that what he thought was the maximum value in his data set should have been a negative value making it the new minimum value in his data set Which statement most likely describes the mean and the median of his new corrected data set A Only the mean will be lower the median must remain the same BOnly the median will be lower the mean must remain the same Both the mean and the median will be lower the mean changed by a greater amount than the median D Both the mean and the median will be lower the median changed by a greater amount than the mean