Statistics Questions

6 19 Student study times A class survey in a large class for first year college students asked About how many hours do you study during a typical week The mean response of the 463 students was as x 13 7 hours 6 Sup pose that we know that the study time follows a Normal distribution with standard deviation o 7 4 hours in mobo the population of all first year students at this university boird a Use the survey result to give a 99 confidence inter val for the mean study time of all first year students b What condition not yet mentioned must be met for onfidence interval to be valid

9 Sample Size and Margin of Error Example 16 1 page 377 described NHANES survey data on the body mass index BMI of 654 young women The mean BMI in the sample was x 26 8 We treated these data as an SRS from a Normally distributed population with standard deviation o 7 5 1 a Suppose that we had an SRS of just 100 young women What would be the margin of error for 95 confidence b Find the margins of error for 95 confidence based on SRSS of 400 young women and 1600 young women c Compare the three margins of error How does increasing the sample size change the margin of error of a confidence interval when the confidence level and population standard deviation remain the same

lo plain the confidence interval for mean ideal weight de scribed in the previous exercise The student answers We can be 95 confident that future samples of adult American women will say that their mean ideal weight is between 137 7 and 140 3 pounds Is this explanation cor rect Explain your answer Hint See the box Interpreting a Confidence Level on page 379

6 5 Find a Critical Value The critical value z for confidence level 75 is not in Table C Use software or Table A of standard Normal probabilities to find z Include in your answer a sketch like Figure 16 3 with C 0 75 and your critical mon Jedi s20gqua arou value z marked on the axis bw pan

companying graph is a histogram of measured mid upper arm circumferences of 297 particular adults ick the icon to view the histogram stogram is point s possible symmetric The histogram is V St O Question 8 O Question 9 O Question 10 S The Frequency 50 40 30 20 10 0 20 Adult Mid Upper Arm Circumferences 24 36 40 28 32 Circumference centimeters 44 48

If X has a binomial distribution with 20 trials and a mean of six then the success probability p is OA 0 30 OB 0 50 OC 0 75 O D This cannot be determined without taking a sample

Opinion polls find that 20 of American adults claim that they don t get enough sleep Suppose you take a random sample of 200 American adults and count the number X in your sample that claim that they never have time to relax The standard deviation of X is O A 40 OB 6 32 O C 5 66 O D 32

An SRS of 25 recent birth records at the local hospital was selected In the sample the average birth weight was x 119 6 ounces Suppose the standard deviation is known to be a 6 5 ounces Assume that in the population of all babies born in this hospital the birth weights follow a Normal distribution with mean Based on the 25 recent birth records the sampling distribution of the sample mean can be represented by OA N H 1 30 OB Nu 6 5 OC N 119 6 6 5 O D N 119 6 1 30

The accompanying graph is a histogram of measured mid upper arm circumferences of 297 particular adults Click the icon to view the histogram The histogram is symmetric The histogram is

A small class has 10 students Seven of the students are male and three are female You write the name of each student on a small card The cards are shuffled thoroughly and you choose one at random observe the name of the student and replace it in the set The cards are thoroughly reshuffled and you again choose a card at random observe the name and replace it in the set This is done a total of five times Let X be the number of cards observed in these four trials with a name corresponding to a male student The random variable X has which probability distribution O A the Normal distribution with mean 3 and variance 1 B the binomial distribution with parameters n 5 and p 0 3 C the binomial distribution with parameters n 5 and p 0 7 O D None of the above

The following table gives the sex and age group of college students at a midwestern university Female Male Total 89 5 668 1 904 1 660 9 321 15 to 17 years 18 to 24 years 25 to 34 years 35 years or older Total 61 4 697 1 589 970 7 317 150 10 365 3 493 2 630 16 638 A student is to be selected at random Given that the selected student is female the conditional probability that she is 25 to 34 years old is O A 0 008 OB 0 545 O C 0 114 O D 0 204

Event A occurs with probability 0 1 Event B occurs with probability 0 6 If A and B are independent then O A P A and B 0 70 B P A or B 0 64 OC P A or B 0 70 O D P A and B 0 64

The high temperature X in degrees Fahrenheit on January days in Columbus Ohio varies according to the Normal distribution with mean 21 and standard deviation 10 The value of P X 10 is O A 0 1357 B 0 7433 O C 0 O D 0 8643

A randomly selected sample of 100 horse owners found that 72 of them feed two flakes of grass hay in the morning and one flake of alfalfa plus one flake of grass hay in the evening to their horses while the rest feed two flakes of grass hay in the morning and one flake of alfalfa plus oat hay in the evening The estimated probability that horse owners feed grass hay in the A M and alfalfa plus oat hay in the P M is O A 0 75 OB 0 50 OC 0 28 O D 0 72

Horses are housed in pasture pipe pens or barn stalls at a local horse barn Let X the number of horses housed in barn stalls Then X is O A an event B a continuous random variable O C a discrete random variable D the sample space

Consider the normal curve in the figure to the right which gives relative frequencies in a distribution of men s heights The distribution has a mean of 70 9 inches and a standard deviation of 2 6 inches 60 62 64 66 68 70 72 74 78 78 height inches a What is the total area under the curve The total area under the curve is Round to the nearest hundredth as needed b Estimate the relative frequency of values less than 68 Choose the correct answer below A 0 13 OB 0 52 OC 0 87 OD 1 00 c Estimate the relative frequency of values greater than 68 Choose the correct answer below OA 1 00 B 0 87 OC 0 13 OD 0 52 d Estimate the relative frequency of values between 68 and 71 Choose the correct answer below A 1 00 OB 0 13 OC 0 61 OD 0 39 e Estimate the relative frequency of values greater than 71 Choose the correct answer below A 0 48 B 1 00 OC 0 17 OD 0 52

4 Select the expression for the probability of Javier volunteers for less than three events each month OP X 3 0 05 OP X 3 0 4 O P X 3 0 2 OP X 3 0 2 O None of the other options 5 Find the probability that Javier volunteers for at least one event each month

A local bakary has determined a probability distribution for the number of cheesecakes that they sell in a given day X sold 0 5 10 15 20 Probability 0 19 0 21 0 13 0 06 What is the probability of selling 15 cheesecakes in a given day What is the probability of selling at least 10 cheesecakes

A random experiment involves drawing a sample of 12 data values from a normally distributed population Th random variable is the third quartile of the data set 37 46 47 51 54 57 58 63 63 68 68 72 Give the random variable Appropriate rounding rules still apply

Which of the following options defines a random variable X that could be helpful in solving the given problem Note that you are not being asked to actually solve the problem A school site selection committee is to be chosen randomly from 16 men and 11 women If the committee consists of 20 members chosen randomly from the 27 what is the probability that exactly of them are men OX the probability of 4 women being chosen for the committee OX the probability of 4 men being chosen for the committee OX the number of people chosen for the committee OX the number of men chosen for the committee

A random variable is defined as a process or variable with a numerical outcome Which of the following are random variables 1 The amount of rain in inches that will fall next Friday in Dallas TX ii The major of a randomly drawn student from Arizona State University iii The number of books purchased next year by your local library Oi only Oii only Oiii only Oi and iii Oii and iii Oi ii and iii

Suppose you have an experiment where you flip a coin three times You then count the number of heads a State the random variable b 1 c I Select an answer rv X the probability that you flip heads rv X number of coins flipped rv X the number of heads flipped when you flip a coin three times rv X the number of heads flipped rv X flipping a coin e number of heads smallest to largest P X number of heads what shape would it be

Javier volunteers in community events each month He does not do more than five events in a month He attends exactly five events 35 of the time four events 25 of the time three events 20 of the time two events 10 of the time one event 5 of the time and no events 5 of the time 1 Define the random variable X Ox is the probability that Javier volunteers for a month OX is an indicator of whether Javier volunteers for a month or not OX is the average number of events in which Javier volunteers for a month Ox is the number of events in which Javier volunteers for a month O None of the other options 2 What values does x take on Ox 0 1 2 3 4 or 5 Ox 1 2 3 4 Ox 2 3 4 or 5 Ox 0 1 2 3 or 4 None of the other options

5 27 The Medical College Admission Test Almost all medical schools in the United States require students to take the Medical College Admission Test MCAT To estimate the mean score of those who took the MCAT on your campus you will obtain the scores of an SRS of students The scores follow a Normal distri bution and from published information you know that the standard deviation is 10 4 Suppose that unknown to you the mean score of those taking the MCAT on your campus is 500 0 a If you choose one student at random what is the probability that the student s score is between 495 and 505 b You sample 25 students What is the sampling dis tribution of their average score x c What is the probability that the mean score of your

3 Guns in School Researchers surveyed 15 624 Amercian high school stu dents grades 9 12 and found that 27 2 of those surveyed were in grade 9 The percent of all American high school students who are in grade 9 is 27 5 The percent of those surveyed who were in grade 9 and had carried a gun to school was 4 5 Is each of the boldface numbers a parameter or a statistic

9 Larger Sample More Accurate Estimate Suppose that in fact the total cholesterol level of all men aged 20 34 follows the Normal distribution with mean 182 milligrams per deciliter mg dL and standard deviation o 37 mg dL a Choose an SRS of 100 m men from this population What is the sampling dis tribution of x What is the probability that x takes a value between 180 and 184 mg dL This is the probability that x estimates within 2 mg dL b Choose an SRS of 1000 men from this population Now what is the prob ability that x falls within 2 mg dL of u The larger sample is much more likely to give an accurate estimate of u

5 29 Daily activity It appears that people who are mildly obese are less active than leaner people One study looked at the average number of minutes per day that people spend standing or walking Among mildly obese people the mean number of minutes of daily ac tivity standing or walking is approximately Normally distributed with mean 373 minutes and standard de viation 67 minutes The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 526 minutes and standard devia tion 107 minutes A researcher records the minutes of activity for an SRS of five mildly obese people and an SRS of five lean people a What is the probability that the mean number of minutes of daily activity of the five mildly obese people exceeds 420 minutes b What is the probability that the mean number of minutes of daily activity of the five lean people ex

5 33 Pollutants in auto exhausts continued The level of nitrogen oxides NOX and nonmethane organ ic gas NMOG in the exhaust over the useful life 150 000 miles of driving of cars of a particular model varies Normally with mean 80 mg mi and standard deviation 4 mg mi A company has 25 cars of this mod el in its fleet What is the level L such that the prob ability that the average NOX NMOG level x for the fleet is greater than L is only 0 01 Hint This requires a backward Normal calculation See page 91 in Chapter if you need to review

5 5 Insurance The idea of insurance is that we all face risks that are unlikely but carry high cost Think of a fire or flood destroying your apartment Insur ance spreads the risk we all pay a small amount and the insurance policy pays a large amount to those few of us whose apartments are damaged An insurance company looks at the records for millions of apartment owners and sees that the mean loss from apartment damage in a year is 130 per person Most of us have no loss but a few lose most of their possessions The 130 is the average loss The company plans to sell renter s insurance for 130 plus enough to cover its costs and profit Explain clearly why it would be unwise to sell only 10 policies Then explain why selling thousands of such policies is a safe business

25 Statistics anxiety What can teachers do to alleviate statistics anxiety in their students To explore this ques tion statistics anxiety for students in two classes was compared In one class the instructor lectured in a for mal manner including dressing formally In the other the instructor was less formal dressed informally was more personal used humor and called on students by their first names Anxiety was measured using a ques tionnaire Higher scores indicate a greater level of anxi ety The mean anxiety score for students in the formal lecture class was 25 40 in the informal class the mean was 20 41 For each of the boldface numbers indicate whether it is a parameter or a statistic Explain your

samplin 7 Generating a Sampling Distribution Let s illustrate the idea of a sampling distribution in the case of a very small sample from a very small population The population is the scores of 10 students on an exam Student Score 1 2 3 4 5 6 7 8 9 10 94 63 81 45 72 72 65 51 75 59 The parameter of interest is the mean score in this population The sample is an SRS of size n 4 drawn from the population The Simple Random Sample applet can be used to select simple random samples of four numbers between 1 and 10 corresponding to the students a Make a histogram of these 10 scores b Find the mean of the 10 scores in the population This is the population mean c Use the Simple Random Sample applet to draw an SRS of size 4 from this population What are the four scores in your sample What is their mean This statistic is an estimate of If you prefer not to use applets use Table B beginning at line 121 to chose an SRS of size 4 from this population d Repeat this process nine more times using the applet or Table B con tinuing on line 121 if you are not using applets Make a histogram of the 10 values of x You are constructing the sampling distribution of x Is the center of your histogram close to How does the shape of this histogram 12

5 11 What Does the Central Limit Theorem Say Asked what the central limit theorem says a student replies As you take larger and larger samples from a population the histogram of the sample values looks more and more Normal Is the student right Explain your answer

7 A teacher believes that 80 of students in the class will want to go on a field trip to the local zoo She performs a hypothesis test to determine if the percentage is less than 80 The teacher samples 50 students and 39 reply that they would want to go to the zoo For the hypothesis test use a 1 level of significance

5 Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have cell phones Five hundred randomly selected adult residents in this city are surveyed to determine whether they have cell phones Of the 500 people surveyed 421 responded yes they own cell phones Using a 95 confidence level compute a confidence interval estimate for the true proportion of adult residents of this city who have cell phones Bound all calculated values to two decimal places and show all five steps of building a confidence interval

1 In a Washington Post University of Maryland poll of 1503 randomly selected US adults 55 said they strongly support gender equity in sports In the following exercises you will construct a 99 confidence interval for the proportion of US adults who strongly support gender equity in sports a Identify the relevant information 1 ii What is the sample size What is the sample proportion Write a sentence to describe what the population parameter is in context b Step 1 Is the sampling distribution of sample proportions approximately normal Why or why not

Use the following information to answer the following four questions A health psychologist is interested in the potential effect that a change in career focus can have on cardiovascular disease for those in high stress jobs She chooses to study divorce lawyers a population that averages a mean systolic blood pressure of 142 with a standard deviation of 13 and measures the blood pressure of 23 former divorce lawyers who switched to environmental law Those 23 lawyers have a mean systolic blood pressure of 131 If all divorce lawyers switched to environmental law what would you expect the mean systolic blood pressure to be with 99 confidence

Recent research suggests that 45 of residents from a certain region have a home phone 94 have a cell phone and 42 of people have both What is the probability that a resident from the region has a a home or cell phone b neither a home phone nor a cell phone c a cell phone but no home phone a The probability of a resident having a home or cell phone is Type an integer or decimal rounded to two decimal places as needed

5 4 pts Complete the following table for the experiment rolling 2 dice and adding their values to find the sum of your roll Determine all possible sums you could roll along with their frequency and relative frequency you may leave these as unreduced fractions Sum Frequency Relative frequency 2 1 36 3 2 36 4 3 3 36 S 4 4 36 6 S 36 7 6 6 36 8 S S 36 9 4 4 36 10 3 3 36 2 2 36 12 1 36 Are the sums all equally likely to be rolled What sum is the most likely to be rolled What sum is the least likely to be rolled

Points 0 of 1 Suppose that 24 of people have a dog 31 of people have a cat and 18 of people own both What is the probability that someone owns a dog or a cat The probability of a person having a dog or a cat is Tyne an integer or a decimal

A check of dorm rooms on a large college campus revealed that 30 had refrigerators 50 had TVs and 25 had both a refrigerator and a TV What s the probability that a randomly selected dorm room has a a refrigerator but no TV b a refrigerator or a TV but not both c neither a refrigerator nor a TV a The probability of having a refrigerator but no TV is C COS

Bam Adebayo Caleb Martin Cody Zeller Dewayne Dedmon Dru Smith Duncan Robinson Gabe Vincent Haywood Highsmith Jamal Cain Jamaree Bouyea Jimmy Butler Kevin Love Kyle Lowry Max Strus Nikola Jovic Omer Yurtseven Orlando Robinson Tyler Herro Udonis Haslem 20 4 9 6 6 5 5 7 2 2 6 4 9 4 4 4 5 4 3 8 22 9 7 7 11 2 11 5 5 5 4 4 3 7 20 1 3 9

Suppose that 25 of people have a dog 18 of people have a cat and 7 of people own both What is the probability that someone owns a dog or a c The probability of a person having a dog or a cat is Typo on integer or a docimal U OT 1

total of M Ms 12 1 7 pts There are 12 M M s in a bag 3 of them are blue 5 are red and 4 of them are green We are going to draw 2 of them from the bag one at a time without replacing them Hint it might help to draw a probability tree to help you with this question Calculate the following probabilities showing your work and giving your solutions as percentages with 2 decimal places Drawing a red M M and then a green M M The probability of drawing a red M M is 5 12 This leaves 11 M Ms left with 4 of them being green making the probability of drawing a green M M 4 11 P red on 1st draw P green on 2nd draw green ad 0 151515 0 151515 100 15 15 Drawing both a blue and red M M their order doesn t matter sample space 12C event space 3c 5c 4c Sc Sc c 3 5 1 5 3 1 15 15 30 drawing any 2 M M s of the same color 120 Sample space event space 3c 5c 4c Sc 3 10 6 19 3 1 1 10 1 1 1 1 6 2 event space sample space 30 1202 30 al 2 0 4545 event space co Sc 3c 4c sample space 12 294 0 2879 Drawing any 2 M M s that are NOT all the same Hint there s a hard way and an easy way to answer this question both equally correct

A consumer organization estimates that over a 1 year period 16 of cars will need to be repaired once 9 will need repairs twice and 1 will require three or more repairs If you own two cars what is the probability that a neither will need repair b both will need repair c at least one car will need repair a The probability that neither will need repair is Do not round b The probability that both will need repair is Do not round c The probability that at least one car will need repair is Do not round Submit quiz

4 pts Complete the following table for the experiment rolling 2 dice and adding their values to find the sum of your roll Determine all possible sums you could roll along with their frequency and relative frequency you may leave these as unreduced fractions Sum Frequency Relative frequency

Suppose that 28 of people have a dog 25 of people have a cat and 19 of people own both What is the probability that someone owns a dog or a cat The probability of a person having a dog or a cat is

35 Multiple choice tests Here is a simple probability model for multiple choice tests Suppose each student has probability p of correctly answering a question cho sen at random from a universe of possible questions A strong student has a higher p than a weak student Answers to different questions are independent a Stacey is a good student for whom p 0 75 Use the Normal approximation to find the probabil ity that Stacey scores between 70 and 80 on a 100 question test b If the test contains 250 questions what is the prob ability that Stacey will score between 70 and 80 You see that Stacey s score on the longer test is more

Suppose that 54 of families living in a certain country own an HDTV and 24 own a computer The Addition Rule might suggest then that 78 of families own either an HDTV or a computer What s wrong with that reasoning Choose the correct answer below CODE OA The sum of the probabilities of the two given events does not equal 1 so this is not a legitimate probability assignment OB The reasoning is correct Thus 78 of families own either an HDTV or a computer OC A family may own both an HDTV and a computer The events are not disjoint so the Addition Rule does not apply OD If one family owns an HDTV or a computer it can influence another family to also own an HDTV or a computer The events are not independent so the Addition Rule does not apply

A survey conducted by the CDC found that 45 9 of U S households used landline phones in 2016 This raises concerns about the accuracy of certain surveys as they depend on random digit dialing to households via landlines Researchers pick eight U S households at random Complete parts a through c a What is the probability that all eight of them have a landline Round to five decimal places as needed

Your list of favorite songs contains ten rock songs eight hip hop songs and seven K pop songs a What is the probability that a randomly played song is a hip hop song b What is the probability that a randomly played song is not K pop a The probability that a randomly played song is a hip hop song is Type an integer or a decimal Do not round