midterm review questions
The accompanying summary statistics and histogram are for the ZIP codes of 500 customers from an internet jewelry store in the United States. What can these statistics tell you about the company's sales? Choose the correct answer below. A.The ZIP codes for purchases from the store are symmetrically distributed around 65,000. B.No information can be gleaned from the summary statistics because ZIP codes are categorical. Your answer is correct .C.The amount of sales is skewed in the direction of higher ZIP codes. D.The amount of sales was spread fairly evenly across the country.
B.No information can be gleaned from the summary statistics because ZIP codes are categorical.
A medical researcher measures the increase in heart rate of patients who are taking a stress test. What kind of variable is the researcher studying? Choose the correct answer below. Identifier variable Categorical variable Ordinal variable Quantitative variable
Quantitative variable
An article reported on a school district's magnet school programs. Of the 1982 qualified applicants, 1056 were accepted, 286 were waitlisted, and 640 were turned away for lack of space. Find the relative frequency for each decision made, and write a sentence summarizing the results.
The relative frequency of accepting qualified students is 1056 -A 286- W 640- D total 1982 RF accepted: 1056/1982 (100)= 53.3% RF Waitlisted: divide the number of waitlisted students by the total number of qualified applicants. 286/ 1982 (100)= 14.4 RF denied: 640/1982 (100)= 32.3 Of the qualified students, 53.3.% were accepted, 14.4% were waitlisted, and 32.3% were turned away due to lack of space
An article reported on a school district's magnet school programs. Of the 1961 qualified applicants, 1071 were accepted, 282 were waitlisted, and 608 were turned away for lack of space. Find the relative frequency for each decision made, and write a sentence summarizing the results. Find the relative frequency of qualified students being accepted.
The relative frequency of accepting qualified students is 1071 -A 282- W 608- D total 1961 RF accepted: 1071/1961 (100)= 54.6% RF Waitlisted: divide the number of waitlisted students by the total number of qualified applicants. 282/ 1961(100)= 14.4 RF denied: 608/1961 (100)= 31.0 Of the qualified students, 54.6% were accepted, 14.4% were waitlisted, and 31% were turned away due to lack of space
An investigation compiled information about recent nonmilitary plane crashes. The causes, to the extent that they could be determined, are summarized in the table to the right. Complete parts a) through c) below. pilot error (A) 49% Pilot Error (weather related) (B) 17% Pilot Error (mechanical related) (C) 55% Other Human Error (D) 77% Weather (E) 66% Mechanical Failure (F) 14% Sabotage (G) 22% Other Causes (H) 11 % a) Is it reasonable to conclude that the weather or mechanical failures caused only about 20% of recent plane crashes? b) Why do the numbers in the table add to 101%?
a. Yes, because there is no possibility for overlap. (14+6=20) b/. The data are given to the nearest whole percent. If several of the categories were rounded up, an extra percentage point could be gained
The Centers for Disease Control lists causes of death in the United States during 1999. (Each person is assigned only one cause of death.) Heart disease: 31.3 cancer= 23.4 circulatory/ stroke= 7.1 respiratory diseases= 6.9 accidents= 4.4 a) Is it reasonable to conclude that heart or respiratory diseases were the cause of approximately 38% of U.S. deaths in 1999? b) What percent of deaths were from causes not listed here?
a. Yes, because there is no possibility for overlap. (31.3+ 6.9= approx. 38) b. 100%- 73.1= 26.9
*** The accompanying histogram shows the running times in minutes of the 150 top-grossing feature films released in a certain year. Complete parts (a) through (c) below. from handout 2 question 7 a) A student plans to see a movie this weekend. Based on these movies, how long would a typical movie be expected to run? b. Would it be surprising to find that the student's movie ran for 2.5 hours (150 minutes)? c) Would the mean or the median run time for all movies be expected to be higher? Why?
a. average 105 minutes b. Yes, because only a small number of the movies in the distribution ran for 150 minutes or more. c. The mean and the median are about equal.
A survey of 12 gas stations produced the following prices for a gallon of regular gasoline. 2.279 2.019 2.079 2.119 2.179 2.059 2.119 2.039 2.159 2.089 2.089 2.139 Make a stem-and-leaf display of these gas prices. Use split stems; for example, use two 2.1 stems, one for prices between $2.10 and $2.149, the other for prices $2.15 to $2.199. *see photo* Describe the shape, center, and spread of this distribution. Is the data symmetric, skewed to the right, or skewed to the left the prices seem to be centered around_________ The prices range from $ ____________ c. What unusual feature do you see?
a. pic b. r skewed c. price center 2.10 gal d. range 2.019 to 2.279 unusual: No stations charged between $ 2.18 and $ 2.27
A survey of 12 gas stations produced the following prices for a gallon of regular gasoline. A survey of 12 gas stations produced the following prices for a gallon of regular gasoline. 2.199 2.019 2.089 2.149 2.279 2.119 2.159 2.119 2.069 2.069 2.079 2.029 a. Make a stem-and-leaf display of these gas prices. Use split stems; for example, use two 2.1 stems, one for prices between $2.10 and $2.149, the other for prices $2.15 to $2.199. b. Describe the shape, center, and spread of this distribution: Is the data symmetric, skewed to the right, or skewed to the left? d. the prices range from__________ What unusual feature do you see?
a. see pic b. The distribution is skewed right c. price center 2.11 gal d. the prices range from $2.019 to $ 2.279 unusual feature- No stations charged between $ 2.20 and $ 2.27
During his 20 seasons playing professional hockey, a certain hockey player scored 50% more points than anyone else who ever played professional hockey. He accomplished this feat while playing in 280 fewer games than the previous record holder. The number of games he played in each season is shown below. Complete parts a through d below. 79, 80, 81, 81, 72, 81, 81, 79, 64, 77, 72, 77, 73, 46, 81, 47, 81, 83, 83, 71 The distribution __________ c) Describe the center and spread of this distribution.
a. see pic b. is unimodal and skewed to the left.
****An article reported on a school district's magnet school programs. Of the 1561 qualified applicants, 470 were black or Hispanic, 233 Asian, and 858 white. Summarize the relative frequency distribution of ethnicity with a sentence or two (in the proper tccontext, of course).
black/hispanic- 470/1561 (100)= 30.1 asian- 233/1561 (100)= 14.9 White 858/1561 (100)= 55
A certain poll question asked, "In the next 5 years comma do you think that things will" get better, stay the same, get worse Is this categorical or quantitative
categorical
The number of annual deaths from tornadoes in a certain region is shown below. 138 95 41 45 550 52 33 29 58 72 124 mean, median, lower quartile (Q1), upper quartile (Q3), range, IQR
sort data 29 33 *41* 45 52 -------*58* 72 95 *124* 138 550 mean: 112.45 (add all numbers/ total) median: 58 (n=11= odd #) exact middle # Q1= 41 (middle of 1st set) Q2 median= 58 Q3= 124 (middle of 2nd set) IQR: 83 (Q1-Q3) Range 521 (max -min) Max: 550 Min: 29
The number of annual deaths from tornadoes in a certain region is shown below. 133 91 39 49 553 62 42 42 64 78 124 a) mean b) median and quartiles c) range and IQR max and min
sort data 39 42 *42*49 62 -------*64* 78 91 *124* 133 553 mean: 116.09 (add all numbers/ total) median: 64 (n=11= odd #) exact middle # Q1= 42 (middle of 1st set) Q2 median= 64 Q3= 124 (middle of 2nd set) IQR: 82 (Q1-Q3) Range 514 (max -min) Max: 553 Min: 39
*** In performing research for an ecology class, students at a college in upstate New York collect data on streams each year. They record a number of biological, chemical, and physical variables, including the stream name, the substrate of the stream (limestone, shale, or mixed), the acidity of the water (pH), the temperature (degrees°C), and the BCI (a numerical measure of biological diversity). 5 Ws how variables, types, unit chart
who - streams what- acidity, temp, BCI, name, substrate of streams when - not specified where- NY streams why- not specified how - not specified *variables* acidity- numerical-pH temp- numerical - (degrees°C) BCI- numerical- not specified substrate of stream- categorical - no unit name- categorical - no unit
For the following description of data - identify the W's - name the variables - specify for each variable whether its use indicates that it should be treated as categorical or quantitative --- if quantitative variable, identify the units in which it was measured (or note that they were not provided). A polling company conducted a representative telephone survey of 1180 of a country's voters during the first quarter of 2007. Among the reported results were the voter's region (Northeast, South, etc.), age, party affiliation, and whether or not the person had voted in the 2006 midterm congressional election.
who- 1180 american voters when- where what- why how- Variables: region (categorical), no units party affiliation (categorical) no units voting status (categorical) no units age (numerical) not specified variable Region, the variable is categorical. The units are are not appropriate since the variable is categorical.
For the following description of data, identify the W's, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided). Researchers investigating the impact of training on sprinting collected data from 728 training sessions during 1991- 1993. They kept track of the runner's age, the number of weeks the training lasted, the type of training (interval, endurance, combined), the level of training the runner had (none, moderate, intense), the weight and sex of runners, and whether the runners exhibited improvement (none, minor, major). who
who- 728 training sessions during 1991- 1993. what- level of training, runner's age, runner's sex, runner's weight, type of training, runners improvement when- between 1991-1993 where- Not specified why- determine effect of training on performance how - Not specified Variables runners age- a quantitative variable and most likely measured in years. duration of training a quantitative variable and measured in weeks. type of training a categorical variable (The units are not appropriate since the variable is categorical) level of training: categorical variable (The units are not appropriate since the variable is categorical) weight: a quantitative variable and most likely measured in lbs sex: categorical variable (The units are not appropriate since the variable is categorical runners improvement: categorical variable (The units are not appropriate since the variable is categorical ___ # of training session (not a variable in this scenario) units N/A duration of the study (not a variable in this scenario) units N/A average improvement: not a variable
Researchers investigating the impact of training on sprinting collected data from 956 training sessions during 1998-2000. They kept track of the runner's age, the number of weeks the training lasted, the type of training (interval, endurance, combined), level of training the runner had (none, moderate, intense), the weight and sex of the runners, and whether the runners exhibited improvement (none, minor, major). 5 Ws how variables
who- 956 training sessions what: duration of training, age, level of training , type of training, weight, sex, level of improvement when 1998-2000 where- not specified why- determine effect of training on performance how - Not specified Variables runners age- numerical- unit: years duration of training- numerical- unit: # of weeks type of training- categorical- no unit level of training- categorical weight- numerical- pounds sex- categorical level of improvement- categorical *not variables* 1. duration of the study 2. # of training sessions 3. average improvement: not a variable
A researcher wondered whether drivers treat bicycle riders differently when they wear helmets. He rigged his bicycle with an ultrasonic sensor that could measure how close each car was that passed him. He then rode on alternating days with and without a helmet. Of the 1000 times that a car passed him, he found that when he wore his helmet, motorists passed 3.67 inches closer to him, on average, than when his head was bare. What is the Who in this study? That is, identify the cases under study. ID the what ID the population
who- Each instance of a car passing a ride what- The distance at which cars pass the bicycle rider and whether or not the rider was wearing a helmet population: All cars which pass bicyclists
The study identified for whom in below: From the given information, the study found that before a meal woman can tell whether the man is cold or warm by looking at his face. In this study 40 undergraduate women were asked to guess the body temperature of 80 men based on photos of their face. In that survey half of the men were cold and the other half were warm, in result it was found that closer a woman was to her next meal the more accurate her guess. who what/purpose population of interest
who- the 40 undergraduate women what/ purpose: The ability to differentiate warm men from cold men. population of interest: all women
****Scientists at a major pharmaceutical firm conducted an experiment to study the effectiveness of an herbal compound to treat the common cold. They exposed each patient to a cold virus, then gave them either the herbal compound or a sugar solution known to have no effect on colds. Several days later they assessed each patient's condition, using a cold severity scale ranging from 0 to 5. They found no evidence of benefits of the compound. 5 Ws how variables, types, unit chart
who-patients what- treatment and cold severity when - not specified where- not specified why- test effectiveness of herbal compound how- through experiments variables treatment- categorical- n/a cold severity- numerical- 0-5 scale
The Postal Service uses five-digit ZIP codes to identify locations to assist in delivering mail. a) In what sense are ZIP codes categorical? b) Is there any ordinal sense to ZIP codes? In other words, does a larger ZIP code tell you anything about a location compared to a smaller ZIP code?
*D.Each ZIP code corresponds to a geographical region.* ----- *E. Yes, since ZIP codes increase from east to west.*
