Statistics Questions

Find the following for the data shown 4 25 32 41 47 62 64 71 73 94 What is the percentile of the data value 71 Round to the nearest whole number Which data value represents the 20th percentile

27 Which of the following standard deviation of approximately 5 A B C D 60 65 70 75 E CH Ma 75 75 75 75 80 90 90 85 80 85 105 here

If all the possible random samples with n 81 scores are selected from a normal population with 80 and 0 9 and the mean is calculated for each sample what is the average of all the sample means 81 80 This cannot be determined with the provided information

26 A random sample of scores at a bowling alley one day gives the following summary statistics n 26 x 132 34 s 10 18 min 113 Q 126 med 134 5 Q3 139 and max 160 How many outliers are there A 0 B 1 C 2 D At least 1 E At least 2

51 The prices at which a particular AP Statistics review book are sold at 92 online sites are summarized in the table below Price 12 25 12 50 12 75 13 00 13 50 14 00 15 00 16 00 19 00 5 11 Frequency 24 21 13 10 2 5 1 Which of the following best describes the distribution of prices A Roughly normal B Skewed left C Skewed right D Skewed both left and right E Bimodal

Calculate the 35th percentile of the data shown X 2 9 15 4 17 1 19 4 24 2 27 3 28 6 30

8 9 10 11 12 13 14 15 16 17 18 19 20 data a Based on the boxplot above what is the value for the Q3

6 7 8 9 10 11 12 13 14 15 16 17 18 data Q Based on the boxplot above identify the 5 number summary

lice officer randomly selected 575 police records of larceny thefts The accompanying data represent the number of offenses for various types of larceny thefts a Construct a probability model for type of larceny theft b Are purse snatching larcenies unusual c Are motor vehicle accessory larcenies unusual Click the icon to view the table a Complete the table below Type of Larceny Theft Pocket picking Purse snatching Shoplifting From motor vehicles Motor vehicle accessories Probability Bicycles From buildings From coin operated machines Round to three decimal places as needed b Choose the correct answer below Data table Type of Larceny Theft Pocket picking Purse snatching Shoplifting From motor vehicles Motor vehicle accessories Bicycles From buildings From coin operated machines Print Number of Offenses C 9 10 Done 135 211 60 39 100 11 X

Find the following for the data shown 2 8 51 56 72 87 95 7 37 52 66 76 91 What is the percentile of the data value 66 Round to the nearest whole number Which data value represents the 20th percentile

A researcher administers a treatment to a sample of participants selected from a population with 90 If a hypothesis test is used to evaluate the effect of the treatment which combination of factors is most likely to result in rejecting the null hypothesis O a sample mean near 80 with a 05 a sample mean near 80 with a 01 a sample mean much different than 80 with a 05 a sample mean much different than 80 with a 01

A sample from a normal population with u 50 and a 6 has a mean of M 48 20 If this specific sample mean corresponds to a z 1 50 then how many scores are in this particular sample O n 36 n 25 16 n n 9

If a researcher decides to reject the null hypothesis using an alpha level of a 05 at the conclusion of a hypothesis test then they would include the statement of p 05 when writing their research report True False

A sample of n 25 scores is selected from a normal population with a mean of u 80 However the calculated mean for this sample of scores is M 81 not the population mean of u 80 This is consistent with the concept of sampling error True False

A sample of n 100 scores is selected from a normal population with u 60 and o 20 It is very unlikely that the sample mean will be greater than M 66 True False

Childhood participation in sports cultural groups and youth groups appears to be related to improved self esteem for adolescents McGee Williams Howden Chapman Martin Kawachi 2006 In a representative study a sample of n 100 adolescents with a history of group participation is given a standardized self esteem questionnaire For the general population of adolescents scores on this questionnaire form a normal distribution with a mean of u 50 and a standard deviation of o 15 The sample of group participation adolescents had an average of M 53 8 a Does this sample provide enough evidence to conclude that self esteem scores for these adolescents are significantly different from those of the general population Use a two tailed test with a 05 Show all four steps part of the steps have already been given fill in the blanks or make your own changes 50 H Step 1 Ho u Step 2 a Step 3 Participation Participation p Z Step 4 Reject Accept the null hypothesis 50 b Compute Cohen s d to measure the size of the difference Is the effect size small medium or big according to the range mentioned in the lecture Cohen 1988 Show your work

On average a sample of n 36 scores from a normal population with d 10 will provide a better estimate of the population mean than a researcher would get with a sample of n 9 scores from a normal population with d 10 True False

100 Childhood participation in sports cultural groups and youth groups appears to be related to improved self esteem for adolescents McGee Williams Howden Chapman Martin Kawachi 2006 In a representative study a sample of n adolescents with a history of group participation is given a standardized self esteem questionnaire For the general population of adolescents scores on this questionnaire form a normal distribution with a mean of u 50 and a standard deviation of o 15 The sample of group participation adolescents had an average of M 53 8 a Does this sample provide enough evidence to conclude that self esteem scores for these adolescents are significantly different from those of the general population Use a two tailed test with a 05 Show all four steps part of the steps have already been given fill in the blanks or make your own changes 50 H Step 1 Ho Step 2 a Step 3 Participation Participation p Z Step 4 Reject Accept the null hypothesis 50 b Compute Cohen s d to measure the size of the difference Is the effect size small medium or big according to the range mentioned in the lecture Cohen 1988 Show your work

From the table of values below create a histogram and decide whether the data is right left or zero symmetrical skewed GPA Frequency 0 0 5 3 0 6 1 0 7 1 1 1 5 14 1 6 2 0 32 2 1 2 5 51 2 6 3 0 3 0 3 5 3 6 4 0 4 1 4 5 Select one 29 16 6 2 a Zero Skewed Symmetrical Ob Right Skewed d Left Skewed

0 In a statistics class there are 23 juniors and 19 seniors 9 of the seniors are females and 15 of the juniors are males A student is selected at random Find the probability of selecting a junior or a female 0 24 42 30 34 42 28 42 32 42

statements is incorrect A 1 1 35 6 4 3 36 11 B 72 373 46 952138 2 7 7 10 39 1259 6 40 0 17 41 6 41 6 means 416 A The distributions have the same mean B The distributions have the same interquartile range C The distributions have the same range D The distributions have the same standard deviation

Use sigma notation to write the sum 1 1 6 1 6 2 IM 1 1 6 3 1 6 15

results by gender are given in the dotplots below 110 712 414 0 1 2 3 4 5 6 0 1 2 3 4 T Female C The ranges are both 6 D The standard deviations T 56 Male Which of the following is a true statement A One distribution is roughly symmetric the other is skewed right B The difference in their means is less than the difference in their medians are roughly the same of results is equal to the sum of the

correspond A B T C 0 D 10 20 10 20 10 30 10 30 10 20 30 40 50 20 30 20 40 50 40 50 S 60 50 30 60 60 60 40 50 60

1 X One element in the dotplot above is labeled X Which of the statements below is true A X has the smallest z score in absolute value of any element in the set B X has the largest z score in absolute value of any element in the set C X has the smallest value of any element in the set D A boxplot will plot X as an isolated point E A back to back stemplot will show two symmetric clusters

Given these parallel boxplots which of the statements below is incorrect A B T 5 10 15 20 25 30 35 40 A The ranges are the same B The interquartile ranges are the same C Both sets have left and right skews D It is possible that set A does not have a symmetric or even a roughly symmetric distribution E It is possible that set A has 1 000 times as many values as set B

3 Which of the following statements about histogram A Two students working with the same set of data may come up with histograms that look different B Histograms of categorical variables can pinpoint clusters and gaps C Unlike other graphs histogram axes do not need to be labeled D Displaying outliers is less problematic when using histograms than when using stemplots E Histograms are more widely used than stemplots or dotplots because histograms display the values of individual observations

Q6 y x f A dx A where A In dx y 2 is x then the value of

The histograms below giv basketball leagues B n 70 71 72 73 74 75 76 Heights inches Which one of the following statements is true A The distribution of heights in League A has a lower mean and lower range than the distribution of heights in League B B The distribution of heights in League A has a lower mean and approximately the same range as the distribution of heights in League B C The distribution of heights in League A has a higher mean and lower range than the distribution of heights in League B D The distribution of heights in League A has a higher mean and higher range than the distribution of heights in League B E The distribution of heights in League A has a higher mean and approximately the same range as the distribution of heights in

For a normal distribution with 43 and o 4 find the following values a the semi interquartile range

Find the area of the region enclosed by f x and the x axis for the given function over the specified interval x 4x 5 x 2 4x 9 x22 f x on 4 5 The area is Type an integer or a simplified fraction

Accessed from Year Make 2006 Ford 2000 Ford 2005 SAAB 1998 Honda 2004 Ford 2001 Chrysler 2004 Honda 2004 Mitsubishi 2006 Honda 2006 Kia jacksonville craigslist org 2003 Dodge 2002 Mitsubishi 2013 Honda 2005 Toyota 2000 Toyota 2003 Mercedes 2004 Ford 1999 Ford 2005 Nissan 2001 Saturn Model Focus Explorer Prelude Mustang GT PT Cruiser Accord Lancer Odyssey Rio Stratus Eclipse Accord Corolla Corolla C240 Explorer F250 Maxima a b Year c Make d Model e Price f Miles g Color h Size on 5 5 2015 Miles Color Size Type 165000 Beige Compact Sedan 3900 1700 3950 199000 Red Full size SUV 123108 Black Full size Sedan 3050 158300 Black Compact Coupe 9500 46000 Black Compact Coupe 1700 167000 Blue Mid size Coupe 1950 123000 Beige Mid size Sedan 2800 145000 White Compact Sedan 8500 131000 Silver Full size Mini van 2500 146818 Silver Compact Sedan 2700 185000 White Mid size Coupe 3600 142025 Black Compact Hatchback 17500 32000 Grey Full size Sedan 5000 129000 Red Compact Sedan 1999 127000 Green Compact Sedan 3700 146035 Black Compact Sedan 2400 213000 Silver Full size SUV 4000 235450 Red Full size Truck 4800 103000 Black Compact Sedan 2600 150000 Silver Compact Coupe 93 i Type j Cylinders 1 Data Classification Classify each variable as qualitative or quantitative Classify each variable as nominal ordinal interval or ratio Classify the quantitative variables as continuous or discrete Explain your classifications 3 points each Example Imagine the data were about homes for rent The variable bedrooms is quantitative ratio data because it has a true zero a value of 0 for that variable means that there are no bedrooms It is discrete random variable because it is a count not a measurement Price Cylinders Condition 4 Good 6 Good 4 Excellent 4 Good 8 Like New 4 Good 4 Excellent 4 Good 6 Excellent 4 Fair 4 Excellent 6 Excellent 4 Excellent 4 Good 4 Fair 6 Good 6 Excellent 8 Good 6 Good 4 Good

The data on the right represent the number of traffic fatalities by seat location and gender Determine P male and P male passenger Are the events male and passenger independent Determine P male P male Round to three decimal places as needed Female Male Total Passenger 32 707 11 724 44 431 6 485 6 269 12 754 39 192 17 993 57 185 Driver Total

mpanying data represent the homework scores for material on Polynomial and Rational Functions for a random sample of students in a college algebra course Complete parts a through h Click the icon to view the data College Algebra Homework Scores 36 28338 28 47 54 60 62 63 65 66 66 69 73 75 77 77 78 78 78 79 79 79 79 79 82 82 84 85 85 86 86 87 89 89 91 O 91 91 93 94 97 97 99 X Skewed right Skewed left Uniform Bell shaped e Determine the sample standard deviation and interquartile range The standard deviation is 13 82 and the interquartile range is 15 5 Round to two decimal places as needed f What is the probability a randomly selected student fails the homework scores less than 70 The probability is 0 25 S Type an integer or a decimal Do not round g What is the probability a randomly selected student earns an A or B on the homework scores 80 or higher Sav The probability is Type an integer or a decimal Do not round

The following table shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years Complete parts a through e macam Weapon Handgun Rifle Shotgun Unknown firearm Knives Hands fists etc Other Interpret this probability Select the correct choice below and fill in the answer box to complete your choice A If 1000 murders were randomly selected exactly of them would have resulted from a rifle or shotgun B If 1000 murders were randomly selected we would expect about 57 of them to have resulted from a rifle or shotgun c What is the probability that a randomly selected murder resulted from a handgun rifle or shotgun P handgun rifle or shotgun Type a decimal rounded to three decimal places as needed Probability 0 475 0 025 0 032 0 143 0 132 0 057 0 136

Suppose x has a distribution with 28 and o 27 LAUSE SALT a If a random sample of size n 35 is drawn find o and P 28 x 30 Round o to two decimal places and the probability to four decimal places o x P 28 x 30 b If a random sample of size n 68 is drawn find o and P 28 x 30 Round o to two decimal places and the probability to four decimal places Hx ox P 28 x 30 Select c Why should you expect the probability of part b to be higher than that of part a Hint Consider the standard deviations in parts a and b The standard deviation of part b is Select part a because of the Select sample size Therefore the distribution about u is

What is the percent abundance of the size 4d nails in this sample Nail Size 14d Number Abundance Mass of Nails 123 77 3 65 11 95 Percent Abundance Weighted 6 8

The accompanying data represent the homework scores for material on Polynomial and Rational Functions for a random sample of students in a college algebra course Complete parts a through h Click the icon to view the data College Algebra Homework Scores 36 47 54 60 62 63 65 66 COME7788 66 69 73 75 22222222 78 79 79 79 79 79 82 82 84 85 85 86 86 87 89 89 91 C 91 91 93 94 97 97 99 X Next question a Construct a relative frequency distribution with a lower class limit of the first class equal to 30 and a class width of 10 Type integers or decimals Do not round Class Relative Frequency

of live multiple delivery births three or more babies in a particular year for women 15 to 54 years old Use the data to complete parts a through d below Age 15 19 20 24 25 29 30 34 35 39 40 44 45 54 Number of Multiple Births Typyr VI b Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was not 30 to 39 years old P not 30 to 39 0 368 Type an integer or decimal rounded to three decimal places as needed c Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was less than 45 years old P less than 45 Type an integer or decimal rounded to three decimal places as needed 96 507 1620 2831 1842 382 11 7

The amount of money spent weekly on cleaning maintenance and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed with mean 609 and standard deviation 37 USE SALT a If 646 is budgeted for next week what is the probability that the actual costs will exceed the budgeted amount Round your answer to four decimal places b How much should be budgeted for weekly repairs cleaning and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0 11 Round your answer to the nearest dollar

The data on the right represent the number of live multiple delivery births three or more babies in a particular year for women 15 to 54 years old Use the data to complete parts a through d below P less than 45 0 984 Type an integer or decimal rounded to three decimal places as needed Age 15 19 20 24 25 29 30 34 35 39 40 44 45 54 Number of Multiple Births 96 507 1620 2831 1842 382 117 d Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was at least 40 years old Interpret this result Is it unusual Find the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was at least 40 years old P at least 40 Tung an integer or decimal rounded to three decimal places as needed

Suppose an x distribution has mean 6 Consider two corresponding x distributions the first based on samples of size n 49 and the second based on samples of size n 81 USE SALT a What is the value of the mean of each of the two x distributions For n 49 x For n 81 Hx b For which x distribution is P x 7 50 smaller Explain your answer O The distribution with n 81 because the standard deviation will be smaller O The distribution with n 49 because the standard deviation will be larger O The distribution with n 49 because the standard deviation will be smaller O The distribution with n 81 because the standard deviation will be larger c For which x distribution is P 4 50 x 7 50 greater Explain your answer O The distribution with n 81 because the standard deviation will be smaller The distribution with n 49 because the standard deviation will be smaller O The distribution with n 49 because the standard deviation will be larger O The distribution with n 81 because the standard deviation will be larger

Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean 28 5 kilograms and standard deviation o 4 4 kilograms Let x be the weight of a fawn in kilograms b The Standard Normal Distribution 0 0 1 3 19 x 0 Convert the following x intervals to z intervals Round your answers to two decimal places a x 30 Z Z 2 c 32 x 35 e z 1 28 x 0 68 of area 95 of area 99 7 of area 1 Convert the following z intervals to x intervals Round your answers to one decimal place d 2 17 Z X 1 00 1 00 2

A university conducted a survey of 371 undergraduate students regarding satisfaction with student government Results of the survey are shown in the table by class rank Complete parts a through d below Click the icon to view the table a If a survey participant is selected at random what is the probability that he or she is satisfied with student government P satisfied Round to three decimal places as needed Data table Satisfied Neutral Not satisfied Total 2 Freshman Sophomore Junior 53 45 64 22 10 25 18 100 73 P 20 15 99 Senior 59 11 29 99 Total 221 63 87 371 O X

Reading test scores are known to follow the normal curve The average reading test score is supposed to be 100 We suspect that the third graders at one of the local schools have a higher average reading score so we take a simple random sample of 10 of these children and find that thei average reading score is 112 Based on this information correctly match the items below a Population i Higher reading test scores b Sample ii c Parameter iii d Statistic iv All reading test scores 112 10 third graders test scores 100 v vi Children at the local school

G The data on the right represent the number of live multiple delivery births three or more babies in a particular year for women 15 to 54 years old Use the data to complete parts a through d below PRO el Yo LONGE ANG Hours Age 15 19 20 24 25 29 30 34 35 39 40 44 45 54 a Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother 30 to 39 years old P 30 to 39 Type an integer or decimal rounded to three decimal places as needed Number of Multiple Births 96 507 1620 2831 1842 382 11 7

How much should a healthy kitten weigh Suppose that a healthy 10 week old domestic kitten should weigh an average of 22 9 ounces with a 95 of data range from 12 0 to x be a random variable that represents the weight in ounces of a healthy 10 week old kitten Assume that x has a distribution that is approximately normal USE SALT a The empirical rule Section 7 1 indicates that for a symmetrical and bell shaped distribution approximately 95 of the data lies within two standard deviations of the mean Therefore a 95 range of data values extending from 20 to 20 is often used for commonly occurring data values Note that the interval from 2o to u 20 is 40 in length This leads to a rule of thumb for estimating the standard deviation from a 95 range of data values Estimating the standard deviation For a symmetric bell shaped distribution standard deviation OZ range high value low value 4 4 where it is estimated that about 95 of the commonly occurring data values fall into this range Estimate the standard deviation of the x distribution Round your answer to two decimal places b What is the probability that a healthy 10 week old kitten will weigh less than 14 ounces Round your answer to four decimal places c What is the probability that a healthy 10 week old kitten will weigh more than 33 ounces Round your answer to four decimal places d What is the probability that a healthy 10 week old kitten will weigh between 14 and 33 ounces Round your answer to four decimal places e A kitten whose weight is in the bottom 16 of the probability distribution of weights is called undernourished What is the cutoff point for the weight of an undernourished kitten Round

The college physical education department offered an advanced first aid course last summer The scores on the comprehensive final exam were normally distributed and the z scores for some of the students are shown below Robert 1 02 OOON Juan Haley 2 14 Juan OOOOO Joel Jan Linda Haley Joel Jan Linda 1 68 a Which of these students scored above the mean Select all that apply Robert 0 00 Robert Juan Haley Joel Jan Linda 0 62 1 68 b Which of these students scored on the mean Select all that apply

The area of the shaded region is Part 2 of 4 0 83

A vending machine automatically pours soft drinks into cups The amount of soft drink dispensed into a cup is normally distributed with a mean of 7 6 ounces and standard deviation of 0 4 ounce Examine the figure below and answer the following questions Area Under a Normal Curve 2 35 13 5 1757 17 34 H 30 20 H 0 34 13 5 2 35 a Estimate the probability that the machine will overflow an 8 ounce cup Round your answer to two decimal places 84 13 x H 0 20 30 68 95 99 7 b Estimate the probability that the machine will not overflow an 8 ounce cup Round your answer to two decimal places 15 85 X M CURS c The machine has just been loaded with 900 cups How many of these cups do you expect will overflow when served