Q&A Hero

Q: 25+ When we transform scores to a distribution that has a mean of 50 and a standard deviation of 10, those scores are called a) z scores. b) t scores. c) T scores. d) stanine scores.

Q: 24 The difference between "probable limits" and "confidence limits" is that the probable limits a) focus on estimating where a particular score is likely to lie using a known population mean. b) estimate the kinds of means that we expect. c) try to set limits that have a .95 probability of containing the population mean. d) There is no difference.

Q: 23+ Assume that your class took an exam last week and the mean and standard deviation of the exam were 85 and 5, respectively. Your instructor told you that 30 percent of the students had a score of 90 or above. You would probably a) think that your instructor was out of her mind. b) decide that your score of 80 would probably fall in the failing range. c) conclude that the scores were not normally distributed. d) conclude that such a set of scores could not possibly happen.

Q: 22+ If we have data that have been sampled from a population that is normally distributed with a mean of 50 and a standard deviation of 10, we would expect that 95% of our observations would lie in the interval that is approximately a) 3070. b) 3550. c) 4555. d) 7090.

Q: 21 We are interested in what the text calls "probable limits" because a) we want to know whether a piece of data is unusual. b) we want to have a good idea what kinds of values to expect. c) we might want to know whether values below some specific value are improbable. d) all of the above

Q: 20+ The formula for calculating the 95% probable limits on an observation is a) ( > 1.96s) b) (s + 1.96) c) ( - 1.96s) d) (  1.96s)

Q: 19+ There are a few z scores that we use often that are worth remembering. The upper 50%, and 97.5 percent of a normal distribution are cut off by z scores of a) 1.0, and 1.64. b) 0.0, and 1.96. c) .50, and .975. d) plus and minus 1.96.

Q: 18 The text discussed setting "probable limits" on an observation. These limits are those which have a a) 50% chance of enclosing the value that the observation will have. b) 75% chance of enclosing the value that the observation will have. c) 80% chance of enclosing the value that the observation will have. d) 95% chance of enclosing the value that the observation will have.

Q: 17 If you are interested in identifying children who are highly aggressive, and you have a normally distributed scale that will do so, you will be particularly interested in a) scores on that scale that are substantially above the mean. b) scores on that scale that are substantially far from the mean. c) scores on that scale that are substantially below the mean. d) any extreme score.

Q: 16+ If we know that the probability for z > 1.5 is .067, then we can say that a) the probability of exceeding the mean by more than 1.5 standard deviations is .067. b) the probability of being more than 1.5 standard deviations away from the mean is .134. c) 86.6% of the scores are less than 1.5 standard deviations from the mean. d) all of the above

Q: 15+ The tables of the standard normal distribution contain only positive values of z. This is because a) the distribution is symmetric. b) z can take on only positive values. c) we aren"t interested in negative values of z. d) probabilities can never be negative.

Q: 14 If behavior problem scores are roughly normally distributed in the population, a sample of behavior problem scores will a) be normally distributed with any size sample. b) more closely resemble a normal distribution as the sample size increases. c) have a mean of 0 and a standard deviation of 1. d) be negatively skewed.

Q: 13 Which of the following is a good reason to convert data to z scores? a) We want to be able to estimate probabilities or proportions easily. b) We think that it is easier for people to work with round numbers. c) We want to make a skewed set of data into a normally distributed set of data. d) all of the above

Q: 12+ A linear transformation of data a) multiplies all scores by a constant and/or adds some constant to all scores. b) is illegal. c) drastically changes the shape of a distribution. d) causes the data to form a straight line.

Q: 11+ A z score of 1.25 represents an observation that is a) 1.25 standard deviation below the mean. b) 0.25 standard deviations above the mean of 1. c) 1.25 standard deviations above the mean. d) both b and c

Q: 10 The symbol p is commonly used to refer to a) any value for the observed variable. b) a value from a standard normal distribution. c) the probability for the occurrence of an observation. d) none of the above

Q: 9 The distribution that is normally distributed with a mean of 0 and a standard deviation of 1 is called a) the normal distribution. b) the standard normal distribution. c) the skewed normal distribution. d) the ideal normal distribution.

Q: 8 Knowing that data are normally distributed allows me to a) calculate the probability of obtaining a score greater than some specified value. b) calculate the probability of obtaining a score of exactly 1. c) calculate what range of values are unlikely to occur by chance. d) both a and c

Q: 7 The ordinate of a normal distribution is often labeled a) frequency. b) X. c) density. d) proportion.

Q: 6+ If behavior problem scores are normally distributed, and we want to say something meaningful about what values are likely and what are unlikely, we would have to know a) the mean. b) the standard deviation. c) the sample size. d) both a and b

Q: 5 If a population of behavior problem scores is reasonably approximated by a normal distribution, we would expect that the X axis would a) have values between 0 and 4. b) have values between -1 and +1. c) have only negative values. d) We cannot say what the values on that axis would be.

Q: 4 The difference between the histogram of 175 behavior problem scores and a normal distribution is a) the normal distribution is continuous, while behavior problem scores are discrete. b) the normal distribution is symmetric, while behavior problem scores may not be. c) the ordinate of the normal distribution is density, the ordinate for behavior problems is frequency. d) Each of the previous choices is correct.

Q: 3+ We know that 25% of the class got an A on the last exam, and 30% got a B. What percent got either an A or a B? a) 25% 30% = 7.5% b) 25% + 30 % = 55% c) 45% d) We cannot tell from the information that is presented.

Q: 2 We care a great deal about areas under the normal distribution because a) they translate directly to expected proportions. b) they are additive. c) they allow us to calculate probabilities of categories of outcomes. d) all of the above

Q: 1+ The normal distribution is a) most frequently observed for the distribution of small sample sizes. b) characterized by a high degree of skewness. c) a distribution with a known shape and other properties. d) the distribution that we would expect for the salaries of basketball players.

Q: 62 Construct two small sets of data that have the same mean, but a different standard deviation.

Q: 61 Given the following distribution, which would be the least useful measure of central tendency? Explain your answer.

Q: 60 Compare the distribution of exam scores for students who did and did not read the textbook prior to taking the exam. Discuss measures of variability and of central tendency.

Q: 59 Answer the following questions based on this distribution of exam scores. a) What is the median? b) Are there outliers? c) Does the distribution seem skewed? If so, is it positively, or negatively skewed?

Q: 58 What happens to the standard deviation when a constant is added to each score? Use the following set of data, and a constant of 2 to illustrate your answer. 1 2 3 4

Q: 57 Create two sets of scores with equal ranges, but different variances.

Q: 56 Create a box plot for the above data.

Q: 55 Based on the same data, calculate: a) The median location b) The median c) The hinge location d) The upper hinge e) The lower hinge f) H spread g) Lower fence h) Upper fence i) Lower adjacent value j) Upper adjacent value

Q: 54 A sample of 20 families reported how many children they have. Answer the following questions based on the summary table below. Number of children 0 1 2 3 4 Number of families 3 6 7 3 1 a) What is the range? b) What is the variance? c) What is the standard deviation?

Q: 53 Answer the following questions based on this set of numbers:1 2 2 3 3 3 4 5a) What is the range?b) What is the variance?c) What is the standard deviation?

Q: 52 There no outliers.

Q: 51 The median of this distribution is 16.

Q: 50 The sample variance is a biased statistic.

Q: 49 Trimmed statistics are calculated based on the entire sample.

Q: 48 The interquartile range is the range of the middle 25% of values.

Q: 47 The variance of a sample is typically a larger value than the standard deviation.

Q: 46 Of all of the measures of variability, the standard deviation is most susceptible to distortion due to outliers.

Q: 45 The difference between the lowest to the highest score in a distribution is the range.

Q: 44 The median is a measure of variability.

Q: 43 Measures of variability refer to the dispersion of data around the mean or the center.

Q: 42 Data points at the extremes of the distribution have a) little effect on the variance. b) distort the usefulness of the median. c) more effect on the variance than scores at the center of the distribution. d) are undoubtedly incorrect.

Q: 41 The population variance is a) an estimate of the sample variance. b) *usually an unknown that we try to estimate. c) calculated exactly like the sample variance. d) a biased estimate.

Q: 40 We normally compute the variance using N " 1 in the denominator because a) it is easier that way. b) it leads to an unbiased estimate of the sample variance. c) it leads to an unbiased estimate of the population variance. d) it overestimates that population variance.

Q: 39 A boxplot is better than a statistic such as the mean when your purpose is a) to describe the central tendency of a population. b) to describe the variability of a population. c) to understand what a distribution of data looks like. d) It is only worthwhile if you care only about medians.

Q: 38 A "hinge" is another word for a) the median. b) a quartile. c) the range. d) boundary.

Q: 37 If I continue to draw observations from a population and recalculate the mean each time I add an observation, the mean will approach _______ as the sample size increases. a) its expected value b) the true population mean c) the median of the population if the population is symmetric d) all of the above

Q: 36 Given the numbers 1, 2, and 3, the standard deviation is a) 0 b) 1 c) 0.667 d) the square of the variance

Q: 35+ The disadvantage of using an interquartile range is that a) it discards too much of the data. b) it removes outliers only extremely high in value. c) the positive and negative deviations balance out. d) it is disproportionately influenced by outliers.

Q: 34 Errors that can lead to outliers can occur in a) measurement. b) data recording. c) data entry. d) all of the above

Q: 33 If the average adult male in the United States is 5" 9" tall, and the standard deviation for height is 2", approximately how many adult males would you expect to be between 5" 7" and 5"11" tall? a) 50% of them b) 66.7% of them c) 75% of them d) 90% of them

Q: 32+ The interquartile range a) is the 50th percentile score in a data set. b) contains as few as 25% of scores or as many as 75% of scores in a data set c) *contains the middle 50% of scores in a data set. d) is the same as the range.

Q: 31 The US Census Bureau collected data on family composition and found that samples from different parts of the country gave very different results for the mean number of family members living in households. If all of the data were combined to one data set, a) the standard deviation of number of family members would probably be very small. b) the standard deviation of number of family members would probably be relatively high. c) the interquartile range would be small. d) the median would equal the mean.

Q: 30 The equation is used to calculate the a) median. b) hinge location. c) outer fence. d) inner fences.

Q: 29+ A data set of intelligence scores was collected from high school seniors. The IQ scores ranged from 82 to 113. Which of the following is probably NOT a reasonable estimate of the standard deviation? a) 6.2 b) 4.7 c) 35.4 d) All of the above are reasonable estimates.

Q: 28 The problem with measuring dispersion by merely averaging all the deviations between each score and the overall mean is that a) positive and negative deviations will balance out. b) squared values make intuitive interpretation difficult. c) dividing by (N-1) gives a biased statistic. d) There are no problems with measuring dispersion this way.

Q: 27+ Which of the following is NOT a method of describing data that reduces the role of outliers on the measurement of a data set's variability? a) interquartile range b) boxplot c) range d) trimmed statistics

Q: 26 The range is a) the difference between the inner fences. b) the H-spread. c) not influenced very much by outliers. d) the difference between the highest and lowest score.

Q: 25+ You would obtain a negative value for the variance if a) all observations were at the mean. b) the distribution is very negatively skewed. c) the distribution if positively skewed. d) you would never obtain a negative variance.

Q: 24 If we know that a set of test scores has a mean of 75 and a standard deviation of 8, we would conclude that a) the average deviation from the mean is about 8 points. b) the average person will have a score of 75 + 8 = 83. c) more people are above 75 than below it. d) You can"t tell anything about how scores lie relative to the mean.

Q: 23+ The standard deviation for the numbers 8, 9, and 10 is a) -3.0 b) 0.0 c) .67 d) 1.0

Q: 22 The university counseling center has treated a large number of students for depression. They find that the standard deviation of depression scores for their pool of students is substantially higher after treatment than before treatment. The most likely explanation is a) some students improved more than others. b) some students improved substantially while others actually got worse. c) depression therapy at the counseling center affects different students differently. d) all of the above

Q: 21 As you increase the number of observations in a sample from 50 to 500, you are most likely to a) leave the mean and standard deviation approximately unchanged. b) increase the variability as the sample size increases. c) decrease the variability as the sample size increases. d) make the shape of the distribution more skewed.

Q: 20 If we multiply a set of data by a constant, such as converting feet to inches, we will a) leave the mean and variance unaffected. b) multiply the mean and the standard deviation by the constant. c) multiply the mean by the constant but leave the standard deviation unchanged. d) leave the mean unchanged but alter the standard deviation.

Q: 19+ Which of the following sets of data is likely to have the smallest standard deviation? a) the distribution of SAT scores for students from your high school b) the distribution of heights of students in an elementary school c) the grade point averages of students from your high school's honors biology class d) the amount that you and your friends pay for college tuition

Q: 18+ People in the stock market refer to a measure called the "standard deviation," although it is calculated somewhat differently from the one discussed here. It is a good guess that this measure refers toa) the riskiness of the stock.b) the value of the stock.c) how much the stock price is likely to fluctuate.d) how much money you are likely to earn from buying that stock.

Q: 17+ If the whiskers on a boxplot are much longer on the right than on the left, we would suspect that the distribution is a) positively skewed. b) negatively skewed. c) symmetric. d) distorted.

Q: 16 Data points that lie outside the whiskers in a boxplot are often referred to as a) incorrect values. b) outliers. c) representative values. d) deviates.

Q: 15+ Data points at the extremes of the distribution have a) little effect on the variance. b) more effect on the variance than scores at the center of the distribution. c) are undoubtedly incorrect. d) distort the usefulness of the median.

Q: 14 The whiskers in a boxplot a) always enclose all of the data points. b) always run from the smaller inner fence to the larger inner fence. c) encompass the H-spread only. d) contain all data points outside the box except the outliers.

Q: 13 In a boxplot the width of the box encompasses a) all of the observed values. b) all but the most extreme values. c) approximately 50% of the observed values. d) the center-most 10% of the values.

Q: 12 The vertical line in the center of a box plot a) represents the sample mean. b) represents the sample median. c) serves to anchor the box. d) can represent anything you want it to.

Q: 11 The difference between s and  is that  is a) the value of the standard deviation in a sample. b) the long range average of the variance over repeated sampling. c) the biased estimate of s. d) the value of the standard deviation in a population.

Q: 10 What do we mean by an unbiased statistic? a) a statistic that equals the sample mean b) a statistic whose average is very stable from sample to sample c) a statistic used to measure racial diversity d) a statistic whose long range average is equal to the parameter it estimates

Q: 9 The variance can best be thought of as the a) average of the squared deviations from the mean. b) average of the absolute deviations from the mean. c) average of the deviations from the median. d) square of the mean.

Q: 8+ When calculating the standard deviation we divide by N-1 rather than N because the result is a) smaller. b) less biased. c) easier to interpret. d) equal to the population mean.