Stat Math – Flashcard
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What is voluntary response sample?
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A sample in which the subjects themselves decide whether to be included in the study.
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Which of the following is typically the important factor to consider when conducting a statistical analysis of data?
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1. Sampling method 2. Context of the data 3. Source of the data
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What does it mean for the findings of a statistical analysis of data to be statistically significant?
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The likelihood of getting these results by chance is very small.
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If we are collecting sample data for a study, the _ that we choose can greatly influence the validity of our conclusions. For example, we can use sound statistical methods to analyze data in voluntary response samples, but the results are not necessarily valid.
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sampling method
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How do parameter and statistic differ?
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A parameter is a numerical measurement of a population; a statistic is a numerical measurement of a sample.
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Which of the following is associated with a parameter?
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Data that were obtained from an entire population.
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Why is a voluntary response sample generally unsuitable for methods of statistics?
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People with special interests are more likely to respond, so the sample is likely to be biased.
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What is the goal of learning statistics?
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To learn to distinguish between statistical conclusions that are likely to be valid and those that are seriously flawed.
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What is a self-interest study?
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A survey in which the sponsor can enjoy monetary or other gains from the results.
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What is the difference between a random sample and a simple random sample?
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With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected.
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Which sampling method divides the population up into sections, randomly selects some of those sections, then choose all the members from the selected sections to study?
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Cluster
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Which sampling method subdivides the population into categories sharing similar characteristics and then selects a sample from each subdivision?
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Stratified
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_is used when subjects are assigned to different groups through a process of random selection.
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Randomization
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Which of the following corresponds to the case when every sample of size n has the same chance of being chosen?
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Simple random sample
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Which characteristic of data is a measure of the amount that the data values vary?
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Variation
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_are sample values that lie very far away from the majority of the other sample values.
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Outliers
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A frequency distribution helps us understand the nature of the distribution of a data set.
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Frequency distribution
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Class width is found by
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subtracting a lower class limit from the next consecutive lower class limit
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In a relative frequency distribution, the frequency of a class is replaced with a proportion or percent.
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relative frequency
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The heights of the bars of a histogram correspond to frequency values.
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frequency
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The bars in a histogram touch.
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touch
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A histogram aids in analyzing the _ of the data.
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shape of the distribution
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A _ histogram has the same shape and horizontal scale as a histogram but the vertical scale is marked with relative frequencies instead of actual frequency.
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relative frequency
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A(n)_distribution has a "bell" shape.
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normal
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What are some advantages of a dotplot over a frequency polygon
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A dotplot allows you to identify the original data values.
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A(n)_uses line segments to connect points located directly above class midpoint values.
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frequency polygon
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A_is a graph of each data value plotted as a point.
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dotplot
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We utilize statistical _ to look for features that reveal some useful or interesting characteristics of the data set.
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graphs
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A _ is a plot of paired data (x,y) and is helpful in determining whether there is a relationship between the two variables.
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scatterplot
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In a graph, if one or both axes begin at some value other than zero, the differences are exaggerated. This bad graphing method is known as _
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a nonzero axis
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When drawings of objects are used to depict data, false impressions can be made. These drawings are called _
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pictographs
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Which of the following is a common distortion that occurs in graphs
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Using a two-dimensional object to represent data that are one-dimensional in nature.
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Why is it important to learn about bad graphs?
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So that we can critically analyze a graph to determine whether it is misleading.
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Methods used that summarize or describe characteristics of data are called _ statistics.
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descriptive
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A value at the center or middle of a data set is a(n) _
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measure of center
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The measure of center that is the value that occurs with the greatest frequency is the _
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mode
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The measure of variation that is very sensitive to extreme values
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Range
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The Range Rule of Thumb roughly estimates the standard deviation of a data set as _
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s=range/4
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For data sets having a distribution that is approximately bell-shaped, _ states that about 68% of all data values fall within one standard deviation from the mean.
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the Empirical Rule
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The square of the standard deviation is called the_
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variance
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When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a _
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z-score
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A data value is considered _ if its z-score is less than -2 or greater than 2
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unusual
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Whenever a data value is less than the mean, _
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the corresponding z-score is negative
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In modified boxplots, a data value is a(n) outlier if it is above Q3+(1.5)(IQR) or below Q1-(1.5)(IQR).
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outlier
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The _ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.
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sample space
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The classical approach to probability requires that the outcomes are _
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equally likely
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As a procedure is repeated again and again, the relative frequency of an event tends to approach the actual probability. This is known as _
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the law of large numbers
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The _ event A occurring are the ratio P(A)/(P(A-)
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actual odds in favor of
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When using the _ always be careful to avoid double-counting outcomes.
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addition rule
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Events that are _ cannot occur at the same time
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disjoint
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P(A) + P(A-) = 1 is one way to express the _
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rule of complementary events
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P(A or B) indicates
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the probability that in a single trial, event A occurs, event B occurs, or they both occur.
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A _ is any event combining two or more simple events.
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compound event
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Describe what the notation P(BlA) represents.
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The probability of event B occurring, given that event A has already occurred.
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A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a _
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tree diagram
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Two events A and B are _ if the occurrence of one does not affect the probability of the occurrence of the other.
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independent
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Selections made with replacement are considered to be _
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independent
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"At least one" is equivalent to_
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"one ore more"
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The complement of "at least one" is _
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"none"
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A conditional probability of an event is a probability obtained with knowledge that some other event has already occurred.
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conditional
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P(BlA) = P(AlB)
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Confusion of the inverse occurs when we incorrectly believe _
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The conditional probability of B given A can be found by _
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assuming that event A has occurred, and then calculating the probability that event B will occur
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Discrete Data
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result when the number of possible values is either a finite number or a "countable" number. (That is, the number of possible values is 0 or 1 or 2, and so on.)
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Continuous Data
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also known as numerical data, result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps
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Determine whether the value given below is from a discrete or continuous data set: When a car is randomly selected and weighed, it is found to weigh 1950.3kg
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A continuous data set because there are infinitely many possible values and those values cannot be counted
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Nominal
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Level of measurement is characterized by data that consist of names, labels, or categories only
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Ordinal
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Data are at the ordinal level of measurement if they can be arranged in some order
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Interval
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Is like the ordinal: Data are at the ordinal level of measurement if they can e arranged in some order with the additional property that the difference between any two data values is meaningful
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Ratio
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The ratio level of measurement is the interval level with the additional property that there is also a natural zero starting point.
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Determine whether the source given below has the potential to create a bias in a statistical study. A certain medical organization tends to oppose the use of meat and dairy products in our diets, and that organization has received hundreds of thousands of dollars in funding from an animal foundation.
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There does appear to be a potential to create a bias. There is an incentive to produce a results that are in line with the organization's creed and that of its funders.
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Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 764 subjects, each was asked how often he or she read a book. The survey subjects were internet users who responded to a question that was posted on a news website.
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It is flawed because it is a voluntary response samples
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Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 759 human resource professionals, each was asked about the importance of the experience of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm.
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It appears to be sound because the data are not biased in any way
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Determine whether the results below appear to have statistical significance, and also determine whether the results have practical significance, In a study of a weight loss program, 7 subjects lost an average of 50lbs. It is found that there is about a 38% chance of getting such results with a diet that has no effect.
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Does the weight loss program have statistical significance? No, the program is not statistically significant because the results are likely to occur by chance. Does the weight loss program have practical significance? Yes, the program is practically significant because the amount of weight loss is large enough to be considered practically significant.
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Several studies showed that after eating chocolate, subject had increased blood levels of antioxidants. Antioxidants have been associated with decreased risk of heart disease. A candy company financed this research. What is wrong with this study?
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Self-interest study
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Based on a study of weights of men and women who are vegetarian, a researcher concludes that eating vegetables causes people to loose weight. Do you agree with this conclusion?
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No, There may be a relationship between a vegetarian diet and weight loss, but that does not mean that one causes the other
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An ad for seat belts claimed that proper usage of seat belts reduces the chance of fatality in a car crash by 300 percent. What is wrong with this statement?
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If seat belts eliminated all fatalities, it would result in a 100% reduction, so it is not possible to reduce fatalities by more than 100%
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An ad for a device used to discourage bike thefts stated that "This device reduces your odds of bike theft by 350 percent." What is wrong with this statement?
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If the device eliminated all bike thefts, it would reduce odds of bike theft by 100% so the 350% figure is misleading.
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Which of the following is typically the least important factor to consider when conducting a statistical analysis of data?
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Formula calculation
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Which of the following is NOT a voluntary response sample?
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Quiz scores from a college level statistics course are analyzed to determine student progress
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Survey questions may be misleading if they are "loaded." To what does "loaded" refer?
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Intentionally worded to elicit a desired response
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Which of the following is NOT a measure of center?
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census
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Which of the following is NOT a characteristic of the mean?
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The mean is called the average by statisticians
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The symbol for standard deviation?
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s
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The symbol for population standard deviation?
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a symbol that resembles a Q
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The symbol for sample variance?
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s squared
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The symbol for population sample variance?
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a symbol that resembles a Q squared
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What is the difference between statistical significance and practical significance? Can a statistical study have statistical significance, but not practical significance?
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Statistical significance is indicated when methods of statistics are used to reach a conclusion that some treatment or finding is effective, but common sense might suggest that the treatment or finding does not make enough of a difference to justify its use or to be practical. Yes, it is possible for a study to have statistical significance but not practical significance.
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In conducting a statistical study, why is it important to consider the source of the data?
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It is important to consider the source of data when conducting a statistical study because some sources may put a spin on the results to obtain favorable results for their gain.
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What is a voluntary response sample, and why is such a sample generally not suitable for a statistical study?
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A voluntary response sample is one in which the subjects themselves decide whether or not to be included in the study. Voluntary response samples are generally not suitable for a statistical study because we can draw valid conclusions only about the specific group of people who chose to participate and the sample may have a bias resulting from participation by those with a special interest in the topic being studied.
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What is meant by the statement "the correlation does not imply causation?"
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A correlation is an association between two variables, such as driving a nice car and owning a nice house. There is a correlation between driving a nice car and owning a nice house, but driving a nice car does not cause a person to own a nice house.
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Determine whether the given source has the potential to create a bias in a statistical study: The Physicians Committee for Responsible Medicine tends to oppose the use of meat and dairy products in our diets, and that organization has received hundreds of thousands of dollars in funding from the Foundation to Support Animal Protection.
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There does appear to be a potential to create bias.
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Determine whether the given source has the potential to create a bias in a statistical study: Data set I in Appendix B includes body measurements obtained by the U.S. Department of Health and Human Services, National Center for Health Statistics.
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There does not appear to be a potential to create a bias.
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Determine whether the given source has the potential to create a bias in a statistical study: Data Set 17 includes word counts obtained by members of the Departments of Psychology at the University of Arizona, Washington University, and the University of Texas at Austin.
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There does not appear to be a potential to create a bias.
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Determine whether the given source has the potential to create a bias in a statistical study: An article in Journal of Nutrition noted that chocolate is rich in flavonoids. The article notes that "regular consumption of foods rich in flavonoids may reduce the risk of coronary heart disease." The study received funding from Mars, Inc., the candy company, and the Chocolate Manufacturers Association.
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There does appear to be a potential to create a bias.
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Determine whether the sampling method appears to be sound or is flawed: A survey of 721 subjects involved the providing of personal information when using Wi-Fi hotspots. The survey subjects were Internet users who responded to a question that was posted on the electronic edition of USA Today.
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The sample is a voluntary response sample and is flawed.
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Determine whether the sampling method appears to be sound or is flawed: In a survey of 109 subjects, each was asked to indicate how many text messages they send and receive each day. The sample consisted of those who chose to respond to the request posted on the StatCrunch Web site.
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The sample is a voluntary response sample and is flawed.
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Determine whether the sampling method appears to be sound or is flawed: In a survey of 514 human resource professionals, each was asked about the importance of the appearance of a job application. The survey subjects were randomly selected by Harris Interactive pollsters.
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The sampling method appears to be sound.
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Determine whether the sampling method appears to be sound or is flawed: In a survey of beliefs about evolution, Gallup pollsters randomly selected and telephoned 1018 adults in the United States.
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The sampling method appears to be sound.
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Determine whether the results appear to have statistical significance, and also determine whether the results have practical significance: In a study of the Marisa Waite diet, four subjects lost an average of 45 pounds. It is found that there is about a 30% of getting such results with a diet that has no effect.
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Because there is a 30% chance of getting such results with a diet that has no effect, it does not appear to have statistical significance, but the average loss of 45 pounds does appear to have practical significance.
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Determine whether the results appear to have statistical significance, and also determine whether the results have practical significance: In a study of the Gender Aide method of gender selection, 1000 users of the method gave birth to 540 boys and 460 girls. There is about a 1% chance that such extreme results would occur if the method had no effect.
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Because there is a 1% chance that such results would occur if the method had no effect, is appears to have statistical significance, but it does not appear to have practical significance.
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Determine whether the results appear to have statistical significance, and also determine whether the results have practical significance: When making random guesses for difficult multiple-choice test questions with possible answers of a, b, c, d, and e, we expect to get about 20% of the answers correct. The Ashton Prep Program claims to have developed a better method of guessing. In a test of that program, guesses were made for 100 answers, and 23 were found to be correct. There is a 23% chance of getting such results if the program has no effect.
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Because there is a 23% chance of getting such results if the program has no effect, it does not appear to have statistical significance. Because the success rate of 23% is not that much better than the 20% rate, it does not appear to have practical significance.
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Determine whether the results appear to have statistical significance, and also determine whether the results have practical significance: Most people have IQ scores between 70 and 130. For $32, you can purchase a computer program from Highiqpro.com that is claimed to increase your IQ score by 10 to 20 points. The program claims to be "the only proven IQ increasing software in the brain training market," but the author of your text could find no data supporting that claim, so let's suppose that these results were obtained: In a study of 12 subjects using the program, the average increase in IQ is 3 IQ points. There is a 25% chance of getting such results if the program has no effect.
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Because there is a 25% chance of getting such results if the program has no effect, it does not appear to have statistical significance. Because the average increase in IQ from the study was only 3 IQ points, while the program claimed to improve your IQ by 10 to 20 points, there does not appear to have practical significance.
