Qmeth Test 1 - 7/25/2020
if r = ________, then a perfect negative linear relation exists between the two quantitative variables
-1
In a recent survey, it was found that the median income of families in country A was $57,700. What is the probability that a randomly selected family has an income greater than $57,700?
.50
Find the probability P(E^c) if P(E)=0.41. The probability P(E^c) is ________
0.59 (P(E^c) = 1 - P(E))
A golf ball is selected at random from a golf bag. If the golf bag contains 3 black balls, 8 orange balls, and 7 yellow balls, find the probability of the following event: The probability that the golf ball is black or orange is __________
0.611 (3+8)/18
Find the probability P(E or F) if E and F are mutually exclusive, P(E)=0.30, and P(F)=0.47. The probability P(E or F) is __________
0.77 (.3 + .47)
1) What is the probability of an event that is impossible? 2) Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is impossible?
1) 0 2) no (When a probability is based on an empirical experiment, a probability of zero does not mean that the event cannot occur. The probability of an event E is approximately the number of times event E is observed divided by the number of repetitions of the experiment, as shown below. Just because the event is not observed, does not mean that the event is impossible.)
The following data represent the dividend yields (in percent) of a random sample of 28 publicly traded stocks. (given a table with 28 numbers) Complete parts 1 to 3 1) compute the five-number summary ______, ______, ________, ______, ______ 2) draw a box plot of the data 3) determine the shape of the distribution from the box plot
1) 0, 0.22, 1.06, 2.41, 3.5 (min, Q1, Q2, Q3, max) (go to stat crunch, click stat - summary stat - columns - request median (Q2) and Q1, Q3 and find min and max) 2) plot based on the five-number summary 3) the distribution is skewed to the right
A probability experiment is conducted in which the sample space of the experiment is S={9,10,11,12,13,14,15,16,17,18,19,20}. Let event E={10,11,12,13,14,15} and event F={14,15,16,17}. 1) List the outcomes in E and F. 2) Are E and F mutually exclusive?
1) 14, 15 (the numbers that are included in both the E and F sets 2) No. E and F have outcomes in common
The least-squares regression equation is y=673.6x+16,372 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7611. 1) predict the median income of a region in which 30% of adults 25 years and older have at least a bachelor's degree 2) In a particular region, 25.9 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $37,117. Is this income higher than what you would expect? Why? This is __________ (lower/higher) than expected because the expected income is __________ dollars 3) interpret the slop of the equation given 4) Explain why it does not make sense to interpret the y-intercept.
1) 36580 (plus 30 into the equation give as x) 2) This is higher than expected because the expected income is 33818 dollars 3) For every percent increase in adults having at least a bachelor's degree, the median income increases by $673.6, on average. 4) It does not make sense to interpret the y-intercept because an x-value of 0 is outside the scope of the model.
An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The frequency histogram to the right gives the results. Use the histogram to complete parts (1) through (6). - the graph shows a histogram that is slowing rising from 2-5 and then slowly decreasing from 5-12 1) What was the most frequent outcome of the experiment? 2) What are the least frequent? 3) How many times did we observe a 6? 4) How many more 9's were observed than 3's? 5) Determine the percentage of time a 6 was observed. 6) Describe the shape of the distribution.
1) 5 (where the histogram bar is highest 2) 2 (where the histogram bar is lowest) 3) 15 (how tall on the y-axis, the bar above 6 is) 4) 5 (how tall the 9 bar is minus how tall the 3 bar is) 5) 15% (answer from #3 divided by the total rolls) 6) skewed right (bc the tail trails off to the right)
Explain the meaning of the following percentiles in parts (1) and (2). 1) The 5th percentile of the weight of males 36 months of age in a certain city is 12.0 kg. 2) The 90th percentile of the length of newborn females in a certain city is 53.8 cm.
1) 5% of 36-month-old males weigh 12.0 kg orless, and 95% of 36 month-old males weigh more than 12.0kg. 2) 90% of newborn females have a length of 53.8 cm orless, and 10% of newborn females have a length that is more than 53.8 cm. *The kth percentile of a set of data is a value such that k percent of the observations are less than or equal to the value.
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following. 1) What percentage of people has an IQ score between 74 and 126? 2) What percentage of people has an IQ score less than 87 or greater than 113? 3) What percentage of people has an IQ score greater than 139?
1) 95% that's two standard deviations away from the mean and so add 13.5+34+34+13.5 2) one standard deviation away and its asking for outside those so add .15+.15+2.35+2.35+ 13.5+13.5 3) that three deviations away from the mean and only above so 0.15 (its important to remember that the graph of the standard deviation shows that 0.15, 2.35, 13.5, 34, 34, 13.5, 2.35, 0.15)
1) What is a closed question? What is an open question? 2) Discuss the advantages and disadvantages of each type of question.
1) A closed question has fixed choices for answers, whereas an open question is a free-response question. 2) Closed questions are easier to analyze, but limit the responses. Open questions allow respondents to state exactly how they feel, but are harder to analyze due to the variety of answers and possible misinterpretation of answers.
A quality-control manager randomly selects 100 bottles of soda that were filled on March 4 to assess the calibration of the filling machine. 1) What is the population of the study? 2) What is the sample of the study?
1) All bottles of soda produced in the plant on March 4 2) the 100 bottles of soda selected in the plant on March 4
1) What is meant by confounding? 2) What is a lurking variable? 3) What is a confounding variable?
1) Confounding in a study occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study. 2) A lurking variable is an explanatory variable that was not considered in a study, but that affects the value of the response variable in the study. In addition, lurking variables are typically related to explanatory variables in the study. 3) A confounding variable is an explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study.
1) What is a cross-sectional study? 2) What is a case-control study? 3) What is the superior observation study? Why?
1) Cross-sectional studies are observational studies that collect information about individuals at a specific point in time or over a very short period of time. 2) Case-control studies are observational studies that are retrospective, meaning that they require individuals to look back in time or require the researcher to look at existing records. 3) Neither study is always the superior to the other. Both have advantages and disadvantages that depend on the situation.
A probability experiment is conducted in which the sample space of the experiment is S={7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}, event E={7, 8, 9, 10} and event G={13, 14, 15, 16}. Assume that each outcome is equally likely. 1) List the outcomes in E and G. 2) Are E and G mutually exclusive?
1) E and G = {} (because they have no overlapping values) 2) Yes, because the events E and G have no outcomes in common.
A probability experiment is conducted in which the sample space of the experiment is S={10,11,12,13,14,15,16,17,18,19,20,21}. Let event E={13,14,15,16}. Assume each outcome is equally likely. List the outcomes in Ec. Find PE^c. 1) List the outcomes in E^c. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 2) P(E^c) = ________
1) E^c = 10, 11, 12, 17, 18, 19, 20, 21 (these are the numbers that are in only one of the data sets not both) 2) P(E^c) = 0.667 (take the number of value in E^c divided by the total values available, so here that's 8/12)
The survey has bias. 1) Which type of Bia best describes the bias in the survey 2) How can the bias be remedied? A polling organization conducts a study to estimate the percentage of households that have both parents sharing equally in household chores. It mails a questionnaire to 1896 randomly selected households across the country and asks the head of each household if he or she has both parents sharing equally in household chores. Of the 1896 households selected, 29 responded.
1) Nonresponse bias 2) The polling organization should try contacting households that do not respond by phone or face-to-face.
Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following. - the scatter diagram shows the dots going in a fairly flat horizontal line and then sloping downward 1) do the two variables have a linear relationship 2) If the relationship is linear do the variables have a positive or negative association?
1) The data points do not have a linear relationship because they do not lie mainly in a straight line. 2) the relationship is not linear
Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following. - the scatter plot shows the boxes slowly slopping downward form the top left corner to the bottom right corner 1) do the two variables have a linear relationship? 2) Do the two variables have a positive or a negative association?
1) The data points have a linear relationship because they lie mainly in a straight line. 2) the two variables have a negative association (because it slopes downward)
The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a well-being test. Complete parts (1) through (4) below. - the table has compute time (in minutes) and well-being score) 1) Which variable is likely the explanatory variable and which is the response variable? 2) describe what the scatter diagram of the data would look like with the following data 3) Determine the linear correlation coefficient between commute time and well-being score. r = _________ 4) Does a linear relation exist between the commute time and well-being index score?
1) The explanatory variable is commute time and the response variable is the well-being score because commute time affects the well-being score. 2) go to stat crunch and click graph and then scatter plot and put commute time (explanatory variable) on the x-axis and the score (response variable) on the y-axis) 3) (this also gives us #2) go to stat crunch and click stat - regression - simple linear - set x and y and compute 4) Yes, there appears to be a negative linear association because r is negative and is less than the negative of the critical value.
1) What does it mean to say that two variables are positively associated? 2) Negatively associated?
1) There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable increases. 2) There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable decreases.
A quality-control manager randomly selects 50 bottles of motor oil that were filled on December 1 to assess the calibration of the filling machine. 1) what is the population in the study? 2) what is the sample in the study?
1) all bottles of motor oil produced in the plant on December 1 2) the 50 bottles of motor oil selected in the plant on December 1
1) what is an observational study? 2) what is a designed experiment? 3) ___________ allows the researcher to claim causation between an explanatory variable and a response variable?
1) an observational study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables 2) a designed experiment is when a researcher assigns individuals to a certain group, intentionally changing the value of an explanatory variable, and then recording the value of the response variable for each group 3) a designed experiment
Define the following terms: 1) experimental unit 2) treatment 3) response variable 4) factor 5) placebo 6) confounding
1) experiment unit = A person, object, or some other well-defined item upon which a treatment is applied 2) treatment = Any combination of the values of the factors (explanatory variables) 3) response variable = The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable 4) factor = A variable whose effect on the response variable is to be assessed by the experimenter 5) placebo = An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication 6) confounding = The effect of two factors (explanatory variables on the response variable) cannot be distinguished.
To predict future enrollment in a school district, fifty households within the district were sampled, and asked to disclose the number of children under the age of five living in the household. The results of the survey are presented in the table. Complete parts (1) through (3) below. 1) Construct a relative frequency distribution of the data 2) What percentage of households has two children under the age of 5?
1) in order to do this you take the number of households per each category of number of children divided the total households 2) for this you take the relative frequency for 2 people having two kids and convert to a percentage by multiplying by 100 3) take the relative frequency for having 1 or 2 kids and add them and then concert to a percentage
Is there an association between party affiliation and gender? The accompanying data represent the gender and party affiliation of registered voters based on a random sample of 810 adults. 1) construct a frequency marginal distribution 2) construct a relative frequency marginal distribution 3) what proportion of registered voters considers themselves to be independent? 4) construct a conditional distribution of party affiliation by gender 5) Draw a bar graph of the conditional distribution found in part Let the red bars (left most) represent Republican, the blue bars (middle) represent Democrat, and the green bars (right most) represent Independent. Choose the correct graph below. 6) Is gender associated with party affiliation? If so, how? Choose the correct answer below.
1) just fill in the boxes at the end of each column and row with the total across 2) again fill in the boxes at tend end of each column and row but now do the percentage that is in that row or column 3) for this, use the calculation from part 2 and select the correct row 4) for this there are just two columns (one female and one male) use the information given originally and find the percentage of each gender that identifies with each group 5) for this use the relative frequencies from part 4 and match them to the right graph accordingly 6) Yes, gender is associated with party affiliation. Males are more likely to be Independents and less likely to be Democrats.
The __________ class limit is the smallest value within the class and the _________ class limit is the largest value within the class
1) lower 2) upper
To help assess student learning in her reform calculus courses, a calculus professor at a university implemented pre- and post-tests for her reform calculus students. A knowledge-gained score was obtained by taking the difference of the two test scores. 1) What type of experimental design is this? 2) What is the response variable in this experiment? 3) What is the treatment?
1) matched pair 2) difference in test score 3) Calculus course
The standard deviation is used in conjunction with the ______ to numerically describe distributions that are bell shaped. The ______ measures the center of the distribution, while the standard deviation measures the ______ of the distribution.
1) mean 2) mean 3) spread
Use the side-by-side boxplots shown to complete parts (1) through (5). (the box plot graph shows two box plots, one box plot, x, is above and is a lot shorter and more scrunched the other is below, y, and a lot more spread out) 1) the median of variable x is _______ 2) the third quartile of variable y is _______ 3) which variable has more dispersion? why? 4) Describe the shape of the variable x. support your position. 5) Describe the shape of the variable y. support your position.
1) median = 80 (where Q2 is on the box plot) 3) Q3 = 100 (where the edge of the box part of y is) 3) Variable y—the interquartile range of variable y is larger than that of variable x. 4) Symmetric—the median is the center of the box and the left and right whiskers are about the same length. 5) Skewed left—the median is right of center in the box and the left whisker is longer than the right whisker.
1) Is the following table an example probability model? 2) What do we call the outcome "blue"? Table = Color/Probability red/0.1 green/0.3 blue/0 brown/0.35 yellow/0.2 orange/0.1
1) no because the probabilities do not sum to 1 2) an impossible event
A frequency distribution lists the ___________ of occurrences of each category of data, while a relative frequency distribution lists the _______ of occurrences of each category of data.
1) number 2) proportion
Compute the range and sample standard deviation for strength of the concrete (in psi). 3910, 4070, 3300, 3000, 2910, 3850, 4070, 4060 1) the range is _______ psi 2) s = _______ psi
1) range = 1160 2) standard deviation = 495.8 (export to stat crunch and click stat - summary stat - column - highlight sample standard deviation and range)
Match the coefficient of determination to the scatter diagram. The scales on the x-axis and y-axis are the same for each scatter diagram. (a) R^2=0.90, (b) R^2=0.12, (c) R^2 = 1 1) scatter diagram I shows a scatter of points (pretty spread out and scattered) with a line that is slightly upward sloping 2) scatter diagram II shows points that are mainly upward slopping but a little scattered around the line 3) scatter diagram III shows almost a perfectly downward sloping line
1) scatter diagram I goes with R^2 = 0.12 2) scatter diagram II goes with R^2 = 0.90 3) scatter diagram III goes with R^2 = 1
Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axis are the same for each scatter diagram. (a) r=0.946, (b) r=0.787, (c) r = 1 1) scatter diagram I has a positive association (slopes upward in a very straight uniform line) 2) scatter diagram II has positive association (slopes upward with a straight, less uniform line) 3) scatter diagram III has a positive association but is much less uniform then the other two (but still resembles a upward sloping line)
1) scatter diagram I goes with r = 1 2) scatter diagram II goes with r = 0.946 3) scatter diagram III goes with r = 0.787
A survey of 900 randomly selected high school students determined that 339 play organized sports. 1) What is the probability that a randomly selected high school student plays organized sports? 2) Interpret this probability.
1) the probability that a randomly selected high school student plays organized sports is 0.377 (take 339/900 and round to the nearest thousands or third decimal) 2) if 1000 high school students were sampled, it would be expected that ABOUT 377 of them play organized sports
A bag of 100 tulip bulbs purchased from a nursery contains 20 red tulip bulbs, 30 yellow tulip bulbs, and 50 purple tulip bulbs. 1) What is the probability that a randomly selected tulip bulb is red? 2) What is the probability that a randomly selected tulip bulb is purple? 3) Interpret these two probabilities.
1) the probability that a randomly selected tulip is red is 0.2 (20/100) 2) the probability that a randomly selected tulip bulb is purple is .5 (50/100) 3) if 100 tulip bulbs were sampled with replacement, one would expect ABOUT 20 bulbs to be red and about 50 of that bulbs to be purple
A polling organization contacts 1598 undergraduates who attend a college and live outside the United States and asks whether or not they had taken a course in conversational English during heir studies. 1) What is the population in the study? 2) What is the sample in the study?
1) undergraduates who attend a college and live outside the United States 2) the 1958 undergraduates who attend a college and live outside the United States
Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all states of a country in a certain year. Complete parts (1) through (4). Q1=272.8, Q2=387.9, Q3= 529.1 1) Provide an interpretation of these results. 2) Determine and interpret the interquartile range. a) The interquartile range is _______ crimes per 100,000 population. b) interpret the interquartile range. 3) a) The violent-crime rate in a certain state of the country in that year was 1,459. Would this be an outlier? The lower fence is __________ crimes per 100,000 population. The upper fence is __________ crimes per 100,000 population. b) the violent-crime rate in a certain state of the country in that year was 1459. would this be an outlier? 4) do you believe that the distribution of violent-crime rates is skewed or symmetric?
1) 25% of the states have a violent-crime rate that is 272.8 crimes per 100,000 population or less. 50% of the states have a violent-crime rate that is 387.9 crimes per 100,000 population or less. 75% of the states have a violent-crime rate that is 529.1 crimes per 100,000 population or less. 2) a) 256.3 interquartile range = Q3-Q1 b) The middle 50% of all observations have a range of 256.3 crimes per 100,000 population. 3) a) lower fence = -111.65 upper fence = 913.55 (lower fence = Q1 - 1.5(IQR), upper fence = Q3 + 1.5(IQR), where IQR is from b, Q3-Q1) b) yes, because it is greater than the upper fence 4) the distribution of violent-crime rates is skewed right (you can see this by drawing out the graph that its slightly skewed)
determine the original set of data 1 | 0 1 3 2 | 1 4 4 7 9 3 | 3 5 5 5 7 9 4 | 0 1
10, 11, 13, 21, 24, 24, 27, 29, 33, 35, 35, 35, 37, 39, 40, 41
What does it mean when a part of the population is under-represented?
A part of the population is under-represented when it is proportionally smaller in a sample than in its population.
What is a residual? What does it mean when a residual is positive?
A residual is the difference between an observed value of the response variable y and the predicted value of y. If it is positive, then the observed value is greater than the predicted value.
Define simple random sampling
A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. The sample is then called a simple random sample.
Describe what an unusual event is. Should the same cutoff always be used to identify unusual events? Why or why not?
An event is unusual if it has a low probability of occurring. The same cutoff should not always be used to identify unusual events. Selecting a cutoff is subjective and should take into account the consequences of incorrectly identifying an event as unusual.
A newspaper asks its readers to call in their opinion regarding the number of books they have read this month. What type of sampling is used?
Convenience
Define statistics A. Statistics encompasses all scientific disciplines in which percentages are used, data are analyzed, and probabilities are found. In addition, statistics references any mathematical model which is reported using percentages or proportions. B. Statistics encompasses all scientific disciplines in which random occurrences are analyzed. In addition, statistics references any random occurrence which is reported using percentages or proportions. C. Statistics is the science of manipulating, reorganizing, and editing information to produce the desired results. In addition, statistics is about providing the required answer with the desired level of confidence. D. Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw a conclusion and answer questions. In addition, statistics is about providing a measure of confidence in any conclusions.
D. Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw a conclusion and answer questions. In addition, statistics is about providing a measure of confidence in any conclusions.
____________ statistics consists of organizing and summarizing information collected, while _________ statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.
Descriptive inferential
In a certain card game, the probability that a player is dealt a particular hand is 0.43. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly 43 times? Why or why not?
The probability 0.43 means that approximately 43 out of every 100 dealt hands will be that particular hand. No, you will not be dealt this hand exactly 43 times since the probability refers to what is expected in the long-term, not short-term.
Explain what each point on the least-squares regression line represents.
Each point on the least-squares regression line represents the predicted y-value at the corresponding value of x.
What does it mean if a statistic is resistant?
Extreme values (very large or small) relative to the data do not affect its value substantially. (a statistic is resistant if it is not sensitive to extreme values)
True or false: correlation implies causation
FALSE; correlation does not imply causation
True or False: A data set will always have exactly one mode.
False
Determine whether the following statement is true or false. The shape of the distribution shown is best classified as skewed left. (the picture included shows a histogram with the higher bars towards the left and a trail to the right)
False (its skewed right because its skewed in the direction of the tail which in this histogram is to the right)
Determine whether the following statement is true or false. Explain; When obtaining a stratified sample, the number of individuals included within each stratum must be equal.
False. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the Strata in the population
The U.S. Department of Housing and Urban Development (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the median?
HUB uses the median because the data are skewed right (they don't want to extreme high values to skew the data as it would skew the mean)
Explain the difference between a single-blind and a double-blind experiment.
In a single-blind experiment, the subject does not know which treatment is received. In a double-blind experiment, neither the subject nor the researcher in contact with the subject knows which treatment is received.
What are the advantages of having a presurvey with open questions to assist in contracting a questionnaire that has closed questions?
the researcher can learn common answers
A study of 6076 adults in public test rooms found that 23% did not wash their hands before exiting. is the value a parameter or a statistic?
the value is a statistic because the 6076 adults in public rest rooms are a sample
What does it mean if r=0?
No linear relationship exists between the variables.
What does it mean when sampling is done without replacement?
Once an individual is selected, the individual cannot be selected again
If E and F are disjoint events, then P(E or F)=
P(E) + P(F)
Let the sample space be S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of the event E={3, 5, 9}.
P(E) = 0.3 P(E) = (number of E)/(number in the sample)
Describe the difference between classical and empirical probability
The empirical method obtains an approximate empirical probability of an event by conducting a probability experiment. The classical method of computing probabilities does not require that a probability experiment actually be performed. Rather, it relies on counting techniques, and requires equally likely outcomes.
Explain the circumstances for which the interquartile range is the preferred measure of dispersion. What is an advantage that the standard deviation has over the interquartile range?
The interquartile range is preferred when the data are skewed or have outliers. An advantage of the standard deviation is that it uses all the observations in its computation.
Why is the median resistant, but the mean is not?
The mean is not resistant because when data are skewed, there are extreme values in the tail, which tend to pull the mean in the direction of the tail. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.
A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why?
The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail.
is the variable discrete or continuous? Volume of a sound
the variable is continuous because it is not countable
In a certain city, the average 20- to 29-year old man is 69.4 inches tall, with a standard deviation of 3.1 inches, while the average 20- to 29-year old woman is 64.3 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 75-inch man or a 70-inch woman? Find the corresponding z-scores. Who is relatively taller, a 75-inch man or a 70-inch woman? Select the correct choice below and fill in the answer boxes to complete your choice. The z-score for the ______(women or man), _______, is ________ (larger or smaller) than the z-score for the _________(women or man), _______, so _____ (he/she) is relatively taller
The z-score for the man, 1.81, is larger than the z-score for the women, 1.5, so he is relatively taller steps for solving: 1) calculate the z-score for the man and women with the formula z-score = (X-u(mean of X))/standard deviation 2) interpret, the one with the higher z-score is relatively taller
Determine if the following statement is true or false. Probability is a measure of the likelihood of a random phenomenon or chance behavior.
True
True or False: In a probability model, the sum of the probabilities of all outcomes must equal 1.
True
Determine whether the following statement is true or false. Explain; Inferences based on voluntary response samples are generally not reliable
True, because it is often the case that the individuals who volunteer do not accurately represent the population
What does it mean to say that the linear correlation coefficient between two variables equals 1? What would the scatter diagram look like?
When the linear correlation coefficient is 1, there is a perfect positive linear relation between the two variables. The scatter diagram would contain points that all lie on a line with a positive slope.
What is a frame?
a frame is a list of the individuals in the population being studied
is the variable qualitative or quantitative? Diver's License class
the variable is qualitative because it is an attribute characteristic
For the histogram on the right determine whether the mean is greater than, less than, or approximately equal to the median. Justify your answer. (the histogram shows the columns slowly getting taller as it goes left to right) Which of the following is correct? A.x<M because the histogram is skewed left. B. x<M because the histogram is skewed right. C. x>M because the histogram is skewed right. D. x=M because the histogram is symmetric. E. x=M because the histogram is skewed left. F. x>M because the histogram is symmetric.
a) x-bar (mean) < M (median) because the histogram is skewed left. (its skewed left because the tail trails off to the left and the mean is smaller than the median because there are extreme low values
the ____________ is the difference between consecutive lower class limits
class width
____________ are the categories by which data are grouped.
classes
To determine customer opinion of their inflight service, Continental Airlines randomly selects 130 flights during a certain week and surveys all passengers on the flights. What type of sampling is used?
cluster
a _____________ is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups
cluster sample
The _______, R^2, measures the proportion of total variation in the response variable that is explained by the least squares regression line.
coefficient of determination
In probability, a(n) ________ is any process that can be repeated in which the results are uncertain.
experiment
A(n) _________ is a person or object that is a member of the population being studied.
individual
An insurance company crashed four cars of the same model at 5 miles per hour. The costs of repair for each of the four crashes were $421, $430, $491, and $243 . Compute the mean, median, and mode cost of repair. Compute the mean cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
mean = 396.25 median = 425.5 mode = none (no number repeats) (Go to stat crunch and click stat - summary stat - column - highlight mean, median, mode)
________ divide data sets in fourths
quartiles
Sony wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 30 customers and asks them about their level of satisfaction with the company. What type of sampling is used?
simple random
A ____________ is a numerical summary of a sample A ____________ is a numerical summary of a population
statistic (sample) parameter (population)
a ___________ is obtained by dividing the population into homogeneous groups and randomly selecting individuals from each group.
stratified sample
To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at General Foods selects every 13th soup can that comes off the assembly line starting with the seventh until she obtains a sample of 30 soup cans. What type of sampling is used?
systematic
Which sampling method does not require a frame? a) systematic b) simple random c) stratified d) cluster e) all of the above sampling methods require a frame
systematic
Which of the following numbers could be the probability of an event? 1, 1.45, 0, 0.25, −0.44, 0.05
the numbers that could be a probability of an event are: 1, 0, 0.25, 0.05
Suppose you toss a coin 100 times and get 81 heads and 19 tails. Based on these results, what is the probability that the next flip results in a tail?
the probability that the next flip results in a tail is approximately 0.19
In a relative frequency distribution, what should the relative frequencies add up to?
the relative frequencies add up to 1
Determine whether the following statement is true or false. Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.
true
Find the population mean or sample mean as indicated. Sample: 24, 15, 1, 11, 14 (is it u or x-bar)
x-bar = 13 (use stat crunch by going to stat - summary stat - column - highlight mean)
You suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. The outcome of the experiment is listed in the following table. Do you think the die is loaded? Why? Value of Die/Frequency 1/43 2/41 3/110 4/46 5/40 6/120
yes, because two of the values have a higher probability of occurring than expected under the assumption of equally likely outcomes
the ___________ represents the number of standard deviations an observation is from the mean
z-score
Suppose that two variables, X and Y, are negatively associated. Does this mean that above-average values of X will always be associated with below-average values of Y? Explain.
No, because association does not mean that every point fits the trend. The negative association only means that above-average values of X are generally associated with below-average values of Y.
True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure.
True, because the standard deviation describes how far, on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.