12.15.2014, Stats 1 combined

2. For a distribution with p, = 40 and o- = 12, find the X value corresponding to each of the following z-scores. a. z= 1.50 b. z = -1.25 c. z=1/3 (10.13.2014 stats ch 6, zscores) (10.13.2014 stats ch 6, zscores)

2. a) x=58, b) x=25 c) x=44

3. In a distribution with p. = 50, a score of X = 42 corresponds to z = -2.00. What is the standard deviation for this distribution? (10.13.2014 stats ch 6, zscores) (10.13.2014 stats ch 6, zscores)

3. a = 4

When you add a constant number to the variables the mean ___(a)___ but the standard deviation ____(b)____. On the other hand if you multiply by a constant then the standard deviation will increase by that change multiple. (10.02.2014, stats lec 4 variability)

(a) mean changes (b) standard deviation does not change

1. Identify the z-score value corresponding to each of the following locations in a distribution. a. Below the mean by 2 standard deviations. b. Above the mean by z standard deviation. c. Below the mean by 1.50 standard deviations. (10.13.2014 stats ch 6, zscores)

. a. z = —2.00 b. z = +0.50 C. z = —1.50

REVIEW EXERCISES 1. a. What is the general goal for descriptive statistics? b. How is the goal served by putting scores in a frequency distribution? c. How is the goal served by computing a measure of central tendency? d. How is the goal served by computing a measure of variability? 2. In a classic study examining the relationship between heredity and intelligence, Robert Tryon (1940) used a selective breeding program to develop separate strains of "smart rats" and "dumb rats." Tryon started with a large sample of laboratory rats and tested each animal on a maze-learning problem. Based on their error scores for the maze, Tryon selected the brightest rats and the dullest rats from the sample. The brightest males were mated with the brightest females. Similarly, the dullest rats were interbred. This process of testing and selective breeding was continued for several generations until Tryon had established a line of maze-bright rats and a separate line of maze-dull rats. The following data represent results similar to those obtained by Tryon. The data consist of maze-learning error scores for the original sample of laboratory rats and the seventh generation of the maze-bright rats. Errors Before Solving Maze Original Rats Seventh Generation Maze-Bright Rats 10 14 7 5 8 7 17 13 12 8 8 6 11 9 20 6 10 4 13 6 15 6 9 8 4 18 10 5 7 9 13 21 6 10 8 6 17 11 14 9 7 8 a. Sketch a polygon showing the distribution of error scores for the sample of original rats. On the same graph, sketch a polygon for the sample of mazebright rats. (Use two different colors or use a dashed line for one group and a solid line for the other.) Based on the appearance of your graph, describe the differences between the two samples. b. Calculate the mean error score for each sample. Does the mean difference support your description from part a? c. Calculate the variance and standard deviation for each sample. Based on the measures of variability, is one group more diverse than the other? Is one group more homogeneous than the other? (10.03.2014 Stats ch 4 textbook extraction/notes)

...

10.25.2014, Stats ch 6 Probability and unit normal table) 1. Under what circumstances is the normal distribution an accurate approximation of the binomial distribution? 2. In the game Rock-Paper-Scissors, the probability that both players will select the same response and tie is p = i, and the probability that they will pick different responses is p = i. If two people play 72 rounds of the game and choose their responses randomly, what is the probability that they will choose the same response (tie) more than 28 times? 3. If you toss a balanced coin 36 times, you would expect, on the average, to get 18 heads and 18 tails. What is the probability of obtaining exactly 18 heads in 36 tosses?

1. When pn and qn are both greater than 10 2. With p = i and q = I, the binomial distribution is normal with p = 24 and a = 4; P(X > 28.5) = Az > 1.13) = 0.1292. 3. X = 18 is an interval with real limits of 17.5 and 18.5. The real limits correspond to z = ±0.17, and a probability of p = 0.1350.

1. What information is provided by the sign (+1-) of a z-score? What information is provided by the numerical value of the z-score? (10.13.2014 stats ch 6, zscores)

1. The sign of the z score tells whether the location is above (+) or below (-) the mean, and the magnitude tells the distance from the mean in terms of the number of standard deviations.

1. A normal-shaped distribution with II = 40 and a = 8 is transformed into z-scores. Describe the shape, the mean, and the standard deviation for the resulting distribution of z-scores. (10.13.2014 stats ch 6, zscores)

1. The z-score distribution would be normal with a mean of 0 and a standard deviation of 1.

1. Place the following sample of n = 20 scores in a frequency distribution table. 6, 9, 9, 10, 8, 9, 4, 7, 10, 9 5, 8, 10, 6, 9, 6, 8, 8, 7, 9

1. X f ──── 10 3 9 6 8 4 7 2 6 3 5 1 4 1 ────

1. For a distribution with p. = 40 and o- = 12, find the z-score for each of the following scores. a. X = 36 b. X = 46 c. X = 56 (10.13.2014 stats ch 6, zscores) (10.13.2014 stats ch 6, zscores)

1. a) z= -0.33 b) 0.5 c) z=1.33

1. In words, explain what is measured by each of the following: a. SS b. Variance c. Standard deviation (10.03.2014 Stats ch 4 textbook extraction/notes)

1. a. SS is the sum of squared deviation scores. b. Variance is the mean squared deviation. c. Standard deviation is the square root of the variance. It provides a measure of the standard distance from the mean.

1. Briefly define each of the following: a. Distribution of sample means b. Expected value of M c. Standard error of M (11.2.2014, stats ch 7, probability )

1. a. The distribution of sample means consists of the sample means for all the possible random samples of a specific size (n) from a specific population. b. The expected value of M is the mean of the distribution of sample means (μ). c. The standard error of M is the standard deviation of the distribution of sample means (σM = σ/n).

1. A population of scores has p. = 73 and a = 8. If the distribution is standardized to create a new distribution with 1.1, = 100 and a = 20, what are the new values for each of the following scores from the original distribution? a. X = 65 b. X = 71 c. X = 81 d. X = 83 (10.13.2014 stats ch 6, zscores)

1. a. z = —1.00, X = 80 b. z = —0.25, X = 95 c. z = 1.00, X = 120 d. z = 1.25, X = 125

The specific addition rule ____1___ rule for addition. This is a mutually exclusive, either one thing or the other will occur. There is also a general addition rule for events that ____2____. "What is the probability of it being a king or a spade", could be a king of spade. You need to subtract the probability of them occurring at the the same time. P(A or B) = P(A) + P(B) -P(A and B), taking away the possibility of getting the king of spades. There is also the specific ____3____ rule. If you want to find out what the probability of two things will occur then it is P(A +B) = (P)A x (P)B. For example what is the probability of flipping coin three times? THen it is 0.5 x 0.5 x 0.5 = 0.125. Also what is probability of slipping 3 times landing on trails, then heads, then tails? p(tail) x p(heads) x p(tails). What about the probability of different types of events? Just _____4___. ___5___ Probability for non independent events. p(black, no replect, then red) = p(blackcard) x p(red | black cards). 26/52 x 26x51. Have to think carefully about this. Almost all fall between -3 and +3 SDs from the mean. We have made an assumption of the theoretical normal curve. de Movire discovered the concept of the normal curve. Fled France for England Late 17th century. Thought of as a gambler's friend. He specialized on chance. He realized that if you ___7___. Carl Gauss was a German mathematician who also discovered a lot about the normal curve. The properties of a normal curve is a theoretical construction. Sometimes called the __8__ curve and other times calls the Gaussian curve. The medium, mode, and mean are in the perfect center. The area under is measured in standard deviations from the curve. The larger section is also called the body and the smaller is always called the tail regardless of where the body is. We have what is called the ___9___ table. You never have to worry about the negative or positive score because it corresponds to the same proportion on either side. When we talk about ranked, it will always going to be to the left of the score. (10.22.2014, Stats lec 6, probability, assignment)

1. either/or 2. are not mutually exclusive 3. multiplication 4. multiply for each of the events 5. Conditional 6. flip coins or anything with probability he found that when the number of events increased the shape of the distributions you begin to have a very smooth curve 7. bell 9. unit normal

Today we are focusing specifically on probability and how it can be applied to Z-Tests. Probability is very related to ___1___ curve. It is the foundation for going into the inferring statistics, where we will be comparing things. The whole idea of the normal curve is that if you get enough numbers you will ___2____ Probability allows you to compare two groups with often a large amount of confidence. To know whether something is by ___3___. There is of course always a certain amount of error which should be accounted from. Basic probability is just the ___4___. You can think of probability in just about anything we do. We will start off normatively and gradually go into inferential statistics. Probability will always be a ratio, the outcomes versus number of all possible events. For example, the probability of selecting a B from A B C D will be p(B tile) = 1 / 4 or 0.25 or 25%. In probability there are different types of events. Independent event which has no influence of the other event, each of those events is independent. One of the easiest ways to think about this is ___6____. The probability for both heads and tails is 0.5 and it does not matter what happens before that, the probability f what will happen the next time will stay exactly the same. This ties into the gambler's fallacy where they think if it happens many times then there is an opportunity for it to happen again. Many casinos will have independent event so thinking that way often will not help the odds. __7___ sample means that all things have same chance of being picked. What this means is that you always out the cherry back before calculating the probability again. Dependent outcomes occurs when they are sampling without ___7___ For example not putting the cherry back which influences the probability of the other one. Example the chance of drawing 1/52=0.25. If you do not replace sampling without replacement then you would get 1/51. (10.22.2014, Stats lec 6, probability, assignment)

1. the normal 2. probably end up with a fairly evenly distributed number. 3. chance or by extra statistics 4. likelihood of an event occurring 5. flipping a coin 6. random 7. sampling without replacement

1. For a sample with a mean of M = 40 and a standard deviation of s = 12, find the z-score corresponding to each of the following X values. X = 43 X = 58 X = 49 X = 34 X = 28 X= 16 (10.13.2014 stats ch 6, zscores)

1. z = 0.25 z = 1.50 z = 0.75 z= —0.50 z= —1.00 z= —2.00

10. A student was asked to compute the mean and standard deviation for the following sample of n = 5 scores: 81, 87, 89, 86, and 87. To simplify the arithmetic, the student first subtracted 80 points from each score to obtain a new sample consisting of 1, 7, 9, 6, and 7. The mean and standard deviation for the new sample were then calculated to be M = 6 and s = 3. What are the values of the mean and standard deviation for the original sample? (10.03.2014 Stats ch 4 textbook extraction/notes)

10. The mean is M = 86 and the standard deviation is s = 3.

10. For the following set of quiz scores: 3, 5, 4, 6, 2, 3, 4, 1, 4, 3 7, 7, 3, 4, 5, 8, 2, 4, 7, 10 a. Construct a frequency distribution table to organize the scores. b. Draw a frequency distribution histogram for these data

10. a. X f 10 1 9 0 8 1 7 3 6 1 5 2 4 5 3 4 2 2 1 1

10. Find the z-score corresponding to a score of X = 60 for each of the following distributions. a. μ = 50 and cr = 20 b. p. = 50 and a = 10 c. μ=50anda=5 d. μ= 50anda=2 (10.13.2014 stats ch 6, zscores)

10. a. z = +0.50 b. z = +1.00 c. z = +2.00 d. z = +5.00

10. For a population with a mean of p = 80 and a standard deviation of a = 12, find the z-score corresponding to each of the following samples. a. M = 83 for a sample of n = 4 scores b. M = 83 for a sample of n = 16 scores c. M = 83 for a sample of n = 36 scores (11.2.2014, stats ch 7, probability )

10. a. σM = 6 points and z = 0.50 b. σM = 3 points and z = 1.00 c. σM = 2 points and z = 1.50

11. Find the X value corresponding to z = 0.25 for each of the following distributions. a. p, = 40 and = 4 b. p. = 40 and a = 8 c. μ= 40andC= 12 d. μ =40and a= 20 (10.13.2014 stats ch 6, zscores)

11. a. X = 41 b. X = 42 c. X = 43 d. X = 45

11. A sample of n = 4 scores has a mean of M = 75. Find the z-score for this sample: a. If it was obtained from a population with p = 80 and if = 10. b. If it was obtained from a population with p = 80 and if = 20. c. If it was obtained from a population with p = 80 and if = 40. (11.2.2014, stats ch 7, probability )

11. a. σM = 5 points and z = 1.00 b. σM = 10 points and z = 0.50 c. σM = 20 points and z = 0.25

12. There are two different formulas or methods that can be used to calculate SS. a. Under what circumstances is the definitional formula easy to use? b. Under what circumstances is the computational formula preferred? (10.03.2014 Stats ch 4 textbook extraction/notes)

12. a. The definitional formula is easy to use when the mean is a whole number and there are relatively few scores. b. The computational formula is preferred when the mean is not a whole number.

12. A population forms a normal distribution with a mean of p = 80 and a standard deviation of a = 15. For each of the following samples, compute the z-score the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a sample of this size. a. M = 84 for n = 9 scores b. M = 84 for n = 100 scores (11.2.2014, stats ch 7, probability )

12. a. With a standard error of 5, M = 84 corresponds to z = 0.80, which is not extreme. b. With a standard error of 1.5, M = 84 corresponds to z = 2.67, which is extreme.

12. A survey given to a sample of 200 college students contained questions about the following variables. For each variable, identify the kind of graph that should be used to display the distribution of scores (histogram, polygon, or bar graph). a. number of pizzas consumed during the previous week b. size of T-shirt worn (S, M, L, XL) c. gender (male/female) d. grade point average for the previous semester e. college class (freshman, sophomore, junior, senior)

12. a. histogram or polygon (ratio scale) b. bar graph (ordinal scale) c. bar graph (nominal scale) d. histogram or polygon (ratio scale) e. bar graph (ordinal scale)

12. A score that is 6 points below the mean corresponds to a z-score of z = -0.50. What is the population standard deviation? (10.13.2014 stats ch 6, zscores)

12. σ = 12

13. A random sample is obtained from a normal population with a mean of p = 30 and a standard deviation of a = 8. The sample mean is M = 33. a. Is this a fairly typical sample mean or an extreme value for a sample of n = 4 scores? b. Is this a fairly typical sample mean or an extreme value for a sample of n = 64 scores? (11.2.2014, stats ch 7, probability )

13. a. With a standard error of 4, M = 33 corresponds to z = 0.75, which is not extreme. b. With a standard error of 1, M = 33 corresponds to z = 3.00, which is extreme.

13. A score that is 12 points above the mean corresponds to a z-score of z = 3.00. What is the population standard deviation? (10.13.2014 stats ch 6, zscores)

13. σ = 4

14. The range is completely determined by the two extreme scores in a distribution. The standard deviation, on the other hand, uses every score. a. Compute the range (choose either definition) and the standard deviation for the following sample of n = 5 scores. Note that there are three scores clustered around the mean in the center of the distribution, and two extreme values. Scores: 0, 6, 7, 8, 14. b. Now we break up the cluster in the center of the distribution by moving two of the central scores out to the extremes. Once again compute the range and the standard deviation. New scores: 0, 0, 7, 14, 14. c. According to the range, how do the two distributions compare in variability? How do they compare according to the standard deviation? (10.03.2014 Stats ch 4 textbook extraction/notes)

14. a. The range is either 14 or 15, and the standard deviation is s = 5. b. After spreading out the two scores in the middle, the range is still 14 or 15 but the standard deviation is now s = 7. c. The two distributions are the same according to the range. The range is completely determined by the two extreme scores and is insensitive to the variability of the rest of the scores. The second distribution has more variability according to the standard deviation, which measures variability for the complete set.

a = 15. What is the probability of obtaining a sample mean greater than M = 97, a. for a random sample of n = 9 people? b. for a random sample of n = 25 people? (11.2.2014, stats ch 7, probability )

14. a. σM = 5, z = 0.60, and p = 0.7257 b. σM = 3, z = 1.00, and p = 0.8413

14. For a population with a standard deviation of o- = 8, a score of X = 44 corresponds to z = —0.50. What is the population mean? (10.13.2014 stats ch 6, zscores)

14. μ = 48

15. For a sample with a standard deviation of s = 10, a score of X = 65 corresponds to z = 1.50. What is the sample mean? (10.13.2014 stats ch 6, zscores)

15. M = 50

15. For the data in the following sample: 8, 1, 5, 1, 5 a. Find the mean and the standard deviation. b. Now change the score of X = 8 to X = 18, and find the new mean and standard deviation. c. Describe how one extreme score influences the mean and standard deviation. (10.03.2014 Stats ch 4 textbook extraction/notes)

15. a. The mean is M = 4 and the standard deviation is s = √9 = 3. b. The new mean is M = 6 and the new standard deviation is √49 = 7. c. Changing one score changes both the mean and the standard deviation.

15. The scores on a standardized mathematics test for 8th-grade children in New York State form a normal distribution with a mean of p = 70 and a standard deviation of a = 10. a. What proportion of the students in the state have scores less than X = 75? b. If samples of n = 4 are selected from the population, what proportion of the samples will have means less than M = 75? c. If samples of n = 25 are selected from the population, what proportion of the samples will have means less than M = 75? (11.2.2014, stats ch 7, probability )

15. a. z = 0.50 and p = 0.6915 b. σM = 5, z = 1.00 and p = 0.8413 c. σM = 2, z = 2.50 and p = 0.9938

15. For the following set of scores Scores: 5, 6,8, 9,5,5,7,5,6,4,6,6,5,7,7,5,4,7,6, 5 a. Place the scores in a frequency distribution table. b. Identify the shape of the distribution.

15. a. ──── X f ──── 9 1 8 1 7 4 6 5 5 7 4 2 ──── b. positively skewed

16. Calculate SS, variance, and standard deviation for the following sample of n = 4 scores: 7, 4, 2, 1. (Note: The computational formula works well with these scores.) (10.03.2014 Stats ch 4 textbook extraction/notes)

16. SS = 21, the sample variance is 7 and the standard deviation is = √7 = 2.65.

16. A population of scores forms a normal distribution with a mean of p = 40 and a standard deviation of o- = 12. a. What is the probability of randomly selecting a score less than X = 34? b. What is the probability of selecting a sample of n = 9 scores with a mean less than M = 34? c. What is the probability of selecting a sample of n = 36 scores with a mean less than M = 34? (11.2.2014, stats ch 7, probability )

16. a. z = -0.50 and p = 0.3085 b. σM = 4, z = -1.50 and p = 0.0668 c. σM = 2, z = -3.00 and p = 0.0013

16. For a sample with a mean of p, = 45, a score of X = 59 corresponds to z = 2.00. What is the sample standard deviation? (10.13.2014 stats ch 6, zscores)

16. s = 7

16. Place the following scores in a frequency distribution table. Based on the frequencies, what is the shape of the distribution? 5, 6, 4, 7, 7, 6, 8, 2, 5, 6 3, 1, 7, 4, 6, 8, 2, 6, 5, 7

16. ──── X f ──── 8 2 7 4 . 6 5 5 3 4 2 3 1 2 2 1 1 ──── Negatively skewed

17. Calculate SS, variance, and standard deviation for the following population of N = 8 scores: 0, 0, 5, 0, 3, 0, 0, 4. (Note: The computational formula works well with these scores.) (10.03.2014 Stats ch 4 textbook extraction/notes)

17. SS = 32, the population variance is 4, and the standard deviation is 2.

17. A population of scores forms a normal distribution with a mean of p = 80 and a standard deviation of if = 10. a. What proportion of the scores have values between 75 and 85? b. For samples of n = 4, what proportion of the samples will have means between 75 and 85? c. For samples of n = 16, what proportion of the samples will have means between 75 and 85? (11.2.2014, stats ch 7, probability )

17. a. z = ±0.50 and p = 0.3830 b. σM = 5, z = ±1.00 and p = 0.6826 c. σM = 2.5, z = ±2.00 and p = 0.9544

17. For a population with a mean of p. = 70, a score of X = 62 corresponds to z = —2.00. What is the population standard deviation? (10.13.2014 stats ch 6, zscores)

17. σ = 4

18. Calculate SS, variance, and standard deviation for the following population of N = 7 scores: 8, 1, 4, 3, 5, 3, 4. (Note: The definitional formula works well with these scores.)| (10.03.2014 Stats ch 4 textbook extraction/notes)

18. SS = 28, the population variance is 4, and the standard deviation is 2.

18. At the end of the spring semester, the Dean of Students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of p = 9 pounds with a standard deviation of o- = 6. The distribution of scores was approximately normal. A sample of n = 4 students is selected and the average weight change is computed for the sample. a. What is the probability that the sample mean will be greater than M = 10 pounds? In symbols, what is p(M > 10)? b. Of all of the possible samples, what proportion will show an average weight loss? In symbols, what is p(M < 0)? c. What is the probability that the sample mean will be a gain of between M = 9 and M = 12 pounds? In symbols, what is p(9 < M < 12)? (11.2.2014, stats ch 7, probability )

18. a. z = 0.33 and p = 0.3707 b. z = 3.00 and p = 0.0013 c. p (0 < z < 1.00) = 0.3413

18. In a population of exam scores, a score of X = 48 corresponds to z = +1.00 and a score of X = 36 corresponds to z = —0.50. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.) (10.13.2014 stats ch 6, zscores)

18. μ = 40 and σ = 8. The distance between the two scores is 12 points which is equal to 1.5

19. Calculate SS, variance, and standard deviation for the following sample of n = 5 scores: 9, 6, 2, 2, 6. (Note: The definitional formula works well with these scores.) (10.03.2014 Stats ch 4 textbook extraction/notes)

19. SS = 36, the sample variance is 9, and the standard deviation is 3.

19. The machinery at a food-packing plant is able to put exactly 12 ounces of juice in every bottle. However, some items such as apples come in variable sizes so it is almost impossible to get exactly 3 pounds of apples in a bag labeled "3 lbs." Therefore, the machinery is set to put an average of p = 50 ounces (3 pounds and 2 ounces) in each bag. The distribution of bag weights is approximately normal with a standard deviation of a = 4 ounces. a. What is the probability of randomly picking a bag of apples that weighs less than 48 ounces (3 pounds)? b. What is the probability of randomly picking n = 4 bags of apples that have an average weight less than M = 48 ounces? (11.2.2014, stats ch 7, probability )

19. a. p(z < -0.50) = 0.3085 b. p(z < -1.00) = 0.1587

19. In a distribution of scores, X = 64 corresponds to z = 1.00, and X = 67 corresponds to z = 2.00. Find the mean and standard deviation for the distribution (10.13.2014 stats ch 6, zscores)

19. μ = 61 and σ = 3. The distance between the two scores is 3 points which is equal to 1.0 standard deviation.

2. Can SS ever have a value less than zero? Explain your answer. (10.03.2014 Stats ch 4 textbook extraction/notes)

2. SS cannot be less than zero because it is computed by adding squared deviations. Squared deviations are always greater than or equal to zero.

2. Describe the distribution of sample means (shape, expected value, and standard error) for samples of n = 36 selected from a population with a mean of p = 100 and a standard deviation of cr = 12.

2. The distribution of sample means will be normal (because n > 30), have an expected value of μ = 100, and a standard error of σM = 12/√36 = 2.

2. What is the advantage of having a mean of p. = 0 for a distribution of z-scores? (10.13.2014 stats ch 6, zscores)

2. With a mean of zero, all positive scores are above the mean and all negative scores are below the mean.

2. For a sample with a mean of M = 80 and a standard deviation of s = 20, find the X value corresponding to each of the following z-scores. z = —1.00 z = —0.50 z = —0.20 z = 1.50 z = 0.80 z = 1.40 (10.13.2014 stats ch 6, zscores)

2. X = 60 X = 70 X = 76 X = 110 X = 96 X = 108

2. Construct a frequency distribution table for the following set of scores. Include columns for proportion and percentage in your table.

2. X f p % ──────────── 9 2 0.10 10% 8 3 0.15 15% 7 5 0.25 25% 6 4 0.20 20% 5 3 0.15 15% 4 2 0.10 10% 3 1 0.05 5% ────────────

2. Describe the location in the distribution for each of the following z-scores. (For example, z = +1.00 is located above the mean by 1 standard deviation.) a. z = — 1.50 b. z = 0.25 c. z = — 2.50 d. z = 0.50 (10.13.2014 stats ch 6, zscores)

2. a. Below the mean by 12 standard deviations. b. Above the mean by y standard deviation. c. Below the mean by 2Z standard deviations. d. Above the mean by 1- standard deviation.

2. A population with a mean of tL = 44 and a standard deviation of a = 6 is standardized to create a new distribution with μ = 50 and a = 10. a. What is the new standardized value for a score of X = 47 from the original distribution? b. One individual has a new standardized score of X = 65. What was this person's score in the original distribution? (10.13.2014 stats ch 6, zscores)

2. a. X = 47 corresponds to z = +0.50 in the original distribution. In the new distribution, the corresponding score is X = 55. b. In the new distribution, X = 65 corresponds to z = +1.50. The corresponding score in the original distribution is X = 53.

2. A distribution has a standard deviation of et = 12. Find the z-score for each of the following locations in the distribution. a. Above the mean by 3 points. b. Above the mean by 12 points. c. Below the mean by 24 points. d. Below the mean by 18 points. (10.13.2014 stats ch 6, zscores)

2. a. z = 0.25 b. z = 1.00 c. z = -2.00 d. z = -1.50

20. The average age for licensed drivers in the county is 1.1 = 40.3 years with a standard deviation of a = 13.2 years. a. A researcher obtained a random sample of n = parking tickets and computed an average age of M = 38.9 years for the drivers. Compute the z-score for the sample mean and find the probability of obtaining an average age this young or younger for a random sample of licensed drivers. Is it reasonable to conclude that this set of n = 16 people is a representative sample of licensed drivers? b. The same researcher obtained a random sample n = 36 speeding tickets and computed an average age of M = 36.2 years for the drivers. Compute z-score for the sample mean and find the probability of obtaining an average age this young or younger for a random sample of licensed drivers. Is it reasonable to conclude that this set of n = people is a representative sample of licensed drivers? (11.2.2014, stats ch 7, probability )

20. a. With a standard error of σM = 3.3, M = 38.9 corresponds to z = -0.42 and p = 0.3372. This is not an unusual sample. It is representative of the population. b. With a standard error of σM = 2.2, M = 36.2 corresponds to z = -1.86 and p = 0.0314. The sample mean is unusually small and not representative.

20. For each of the following populations, would a score of X = 50 be considered a central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)? a. p, = 45 and cr = 10 b. p, = 45 and o- = 2 c. μ =90anda=20 d. = 60 and o- = 20 (10.13.2014 stats ch 6, zscores)

20. a. central (z = 0.50) b. extreme (z = 2.50) c. extreme (z = -2.00) d. central (z = -0.50)

21. People are selected to serve on juries by randomly picking names from the list of registered voters. The average age for registered voters in the county is 1.1 = 44.3 years with a standard deviation of a = 12.4. A statistician computes the average age for a group of n = 12 people currently serving on a jury and obtains a mean of M = 48.9 years. a. How likely is it to obtain a random sample of n = 12 jurors with an average age equal to or greater than 48.9? b. Is it reasonable to conclude that this set of n = 12 people is not a representative random sample of registered voters? (11.2.2014, stats ch 7, probability )

21. a. With a standard error of 3.58 this sample mean corresponds to a z score of z = 1.28. A z score this large (or larger) has a probability of p = 0.1003. b. A sample mean this large should occur only 1 out of 10 times. This is not a very representative sample.

21. A distribution of exam scores has a mean of p. = 80. a. If your score is X = 86, which standard deviation would give you a better grade: a = 4 Cr = 8? b. If your score is X = 74, which standard deviation would give you a better grade: Cr = 4 or Cr = 8? (10.13.2014 stats ch 6, zscores)

21. a. σ = 4 b. σ = 8

3. A distribution of English exam scores has p. = 70 and a = 4. A distribution of history exam scores has p. = 60 and a = 20. For which exam would a score of X = 78 have a higher standing? Explain your answer. (10.13.2014 stats ch 6, zscores)

3. For the English exam, X = 78 corresponds to z = 2.00, which is a higher standing than z = 0.90 for the history exam.

3. Is it possible to obtain a negative value for the variance or the standard deviation? (10.03.2014 Stats ch 4 textbook extraction/notes)

3. Standard deviation and variance are measures of distance and are always greater than or equal to zero.

22. In an extensive study involving thousands of British children, Arden and Plomin (2006) found significantly higher variance in the intelligence scores for males than for females. Following are hypothetical data, similar to the results obtained in the study. Note that the scores are not regular IQ scores but have been standardized so that the entire sample has a mean of M = 10 and a standard deviation of s = 2. a. Calculate the mean and the standard deviation for the sample of n = 8 females and for the sample of n = 8 males. b. Based on the means and the standard deviations, describe the differences in intelligence scores for males and females. Female Male 9 8 11 10 10 11 13 12 8 6 9 10 11 14 9 9 (10.03.2014 Stats ch 4 textbook extraction/notes)

22. a. For the females, M = 10 and s = 1.60. For the males, M = 8 and s = 2.45. b. The males and females have the same mean IQ score but the male's scores are more variable.

22. Find the requested percentiles and percentile ranks for the following distribution of quiz scores for a class of N = 40 students. X f cf c% 20 2 40 100.0 19 4 38 95.0 18 6 34 85.0 17 13 28 70.0 16 6 15 37.5 15 4 9 22.5 14 3 5 12.5 13 2 2 5.0 a. What is the percentile rank for X = 15? b. What is the percentile rank for X = 18? c. What is the 15th percentile? d. What is the 90th percentile?

22. a. The percentile rank for X = 15 is 17.5%. b. The percentile rank for X = 18 is 77.5%. c. The 15th percentile is X = 14.75. d. The 90th percentile is X = 19.

22. For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer. a. A score of X = 56, on an exam with p, = 50 and Cr = 4; or a score of X = 60 on an exam with p, = 50 and cr = 20. b. A score of X = 40, on an exam with 1.1, = 45 and Cr = 2; or a score of X = 60 on an exam with u= 70 and u= 20. c. A score of X = 62, on an exam with p. = 50 and Cr = 8; or a score of X = 23 on an exam with = 20 and a = 2. (10.13.2014 stats ch 6, zscores)

22. a. X = 56 corresponds to z = 1.50 (better grade), and X = 60 corresponds to z = 0.50. b. X = 60 corresponds to z = -0.50 (better grade), and X = 40 corresponds to z = -2.50. c. X = 62 corresponds to z = 1.50, and X = 23 also corresponds to z = 1.50. The two scores have the same relative position and should receive the same grade.

23. In the Preview section at the beginning of this chapter we reported a study by Wegesin and Stern (2004) that found greater consistency (less variability) in the memory performance scores for younger women than for older women. The following data represent memory scores obtained for two women, one older and one younger, over a series of memory trials. a. Calculate the variance of the scores for each woman. b. Are the scores for the younger woman more consistent (less variable)? Younger Older 8 7 6 5 6 8 7 5 8 7 7 6 8 8 8 5 (10.03.2014 Stats ch 4 textbook extraction/notes)

23. a. For the younger woman, the variance is s2 = 0.786. For the older woman, the variance is s2 = 1.696. b. The variance for the younger woman is only half as large as for the older woman. The younger woman's scores are much more consistent.

23. Use interpolation to find the requested percentiles and percentile ranks requested for the following distribution of scores. X f fc f c% 14-15 3 50 100 12-13 6 47 94 10-11 8 41 82 8-9 18 33 66 6-7 10 15 30 4-5 4 5 10 2-3 1 1 2 a. What is the percentile rank for X = 5? b. What is the percentile rank for X = 12? c. What is the 25th percentile? d. What is the 70th percentile?

23. a. The percentile rank for X = 5 is 8%. b. The percentile rank for X = 12 is 85%. c. The 25th percentile is X = 7. d. The 70th percentile is X = 10.

23. A distribution with a mean of p, = 62 and a standard deviation of o• = 8 is transformed into a standardized distribution with p, = 100 and = 20. Find the new, standardized score for each of the following values from the original population. a. X = 60 b. X = 54 c. X = 72 d. X = 66 (10.13.2014 stats ch 6, zscores)

23. a. X = 95 (z = -0.25) b. X = 80 (z = -1.00) c. X = 125 (z = 1.25) d. X = 110 (z = 0.50)

24. The following frequency distribution presents a set of exam scores for a class of N = 20 students. X f cf c% 90-99 4 20 100 80-89 7 16 80 70-79 4 9 45 60-69 3 5 25 50-59 2 2 10 a. Find the 30th percentile. b. Find the 88th percentile. c. What is the percentile rank for X = 77? d. What is the percentile rank for X = 90?

24. a. The 30th percentile is X = 72. b. The 88th percentile is X = 93.5. c. The percentile rank for X = 77 is 40%. d. The percentile rank for X = 90 is 81%.

24. A distribution with a mean of p, = 56 and a standard deviation of o- = 20 is transformed into a standardized distribution with p„ = 50 and a = 10. Find the new, standardized score for each of the following values from the original population. a. X = 46 b. X = 76 c. X = 40 d. X = 80 (10.13.2014 stats ch 6, zscores)

24. a. X = 45 (z = -0.50) b. X = 60 (z = 1.00) c. X = 42 (z = -0.80) d. X = 62 (z = 1.20)

25. Construct a stem and leaf display for the data in problem 6 using one stem for the scores in the 60s, one for scores in the 50s, and so on.

25. 1│796 2│0841292035826 3│094862 4│543 5│3681 6│4

26. A set of scores has been organized into the following stem and leaf display. For this set of scores: a. How many scores are in the 70s? b. Identify the individual scores in the 70s. c. How many scores are in the 40s? d. Identify the individual scores in the 40s. 3 8 4 60 5 734 6 81469 7 2184 8 247

26. a. 4 b. 72, 71, 78, and 74 c. 2 d. 46 and 40

27. Use a stem and leaf display to organize the following distribution of scores. Use seven stems with each stem corresponding to a 10-point interval. Scores: 28, 54, 65, 53, 81 45, 44, 51, 72, 34 43, 59, 65, 39, 20 53, 74, 24, 30, 49 36, 58, 60, 27, 47 22, 52, 46, 39, 65

27. 2 │80472 3 │49069 4 │543976 5 │4319382 6 │5505 7 │24 8 │1

3. A sample is selected from a population with a mean of p = 40 and a standard deviation of o- = 8. a. If the sample has n = 4 scores, what is the expected value of M and the standard error of M? b. If the sample has n = 16 scores, what is the expected value of M and the standard error of M? (11.2.2014, stats ch 7, probability )

3. a. The expected value is μ = 40 and σM = 8/√4 = 4. b. The expected value is μ = 40 and σM = 8/√16 = 2.

3. A distribution has a standard deviation of a = 6. Describe the location of each of the following z-scores in terms of position relative to the mean. For example, z = +1.00 is a location that is 6 points above the mean. a. z = +2.00 b. z = +0.50 c. z = -2.00 d. z = -0.50 (10.13.2014 stats ch 6, zscores)

3. a. above the mean by 12 points b. above the mean by 3 points c. below the mean by 12 points d. below the mean by 3 points

3. Find each value requested for the distribution of scores in the following table. a.n b.EX c. EX^2 x f 5 2 4 3 3 5 2 1 1 1

3. a. n = 12 b. ΣX = 40 c. ΣX2 = 148

3. For a population with g. = 30 and a = 8, find the z-score for each of the following scores: a. X = 32 b. X = 26 c. X = 42 (10.13.2014 stats ch 6, zscores)

3. a. z = +0.25 b. z = —0.50 c. z = +1.50

3. For a sample with a mean of M = 85, a score of X = 80 corresponds to z = —0.50. What is the standard deviation for the sample? (10.13.2014 stats ch 6, zscores)

3. s = 10

4. What does it mean for a sample to have a standard deviation of zero? Describe the scores in such a sample. (10.03.2014 Stats ch 4 textbook extraction/notes)

4. A standard deviation of zero indicates there is no variability. In this case, all of the scores in the sample have exactly the same value.

4. For a sample with a standard deviation of s = 12, a score of X = 83 corresponds to z = 0.50. What is the mean for the sample? (10.13.2014 stats ch 6, zscores)

4. M = 77

4. The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not normal? (11.2.2014, stats ch 7, probability )

4. The distribution of sample means will not be normal when it is based on small samples (n < 30) selected from a population that is not normal.

4. A distribution of English exam scores has p. = 50 and a = 12. A distribution of history exam scores has p. = 58 and a = 4. For which exam would a score of X = 62 have a higher standing? Explain your answer. (10.13.2014 stats ch 6, zscores)

4. The score X = 62 corresponds to z = +1.00 in both distributions. The score has exactly the same standing for both exams.

4. For a population with p. = 50 and a = 12, find the X value corresponding to each of the following z-scores: a. z = —0.25 b. z = 2.00 c. z = 0.50 (10.13.2014 stats ch 6, zscores)

4. a. X = 47 b. X = 74 c. X = 56

4. In a distribution with o- = 12, a score of X = 56 corresponds to z = -0.25. What is the mean for this distribution? (10.13.2014 stats ch 6, zscores)

4. p. = 59

5. Explain why the formulas for sample variance and population variance are different. (10.03.2014 Stats ch 4 textbook extraction/notes)

5. Without some correction, the sample variance underestimates the variance for the population. Changing the formula for sample variance (using n - 1 instead of N) is the necessary correction

5. A population has a standard deviation of r = 30. a. On average, how much difference should exist between the population mean and the sample mean for n = 4 scores randomly selected from the population? b. On average, how much difference should exist for a sample of n = 25 scores? c. On average, how much difference should exist for a sample of n = 100 scores? (11.2.2014, stats ch 7, probability )

5. a. Standard error = 30/4 = 15 points b. Standard error = 30/25 = 6 points c. Standard error = 30/100 = 3 points

5. A sample has a mean of M = 30 and a standard deviation of s = 8. a. Would a score of X = 36 be considered a central score or an extreme score in the sample? b. If the standard deviation were s = 2, would X = 36 be central or extreme? (10.13.2014 stats ch 6, zscores)

5. a. X = 36 is a central score corresponding to z = 0.75. b. X = 36 would be an extreme score corresponding to z = 3.00.

6. For a population with a mean of p = 70 and a standard deviation of o = 20, how much error, on average, would you expect between the sample mean (M) and the population mean for each of the following sample sizes? a. n = 4 scores b. n = 16 scores c. n = 25 scores (11.2.2014, stats ch 7, probability )

6. a. 20/4 = 10 points (box is square root) b. 20/16 = 5 points c. 20/25 = 4 points

6. A population has a mean of p. = 80 and a standard deviation of if = 20. a. Would a score of X = 70 be considered an extreme value (out in the tail) in this sample? b. If the standard deviation were if = 5, would a score of X = 70 be considered an extreme value? (10.03.2014 Stats ch 4 textbook extraction/notes)

6. a. No. X = 70 is 10 points away from the mean, only ½ of the standard deviation. b. Yes. With s = 5, 10 points is equal to a distance of 2 standard deviations.

The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. In the situation of a sample you would subtract 1 from the number dividing for the mean of the squared numbers because of a concept called degrees of freedom which mainly is that there is a tendency for deviations to be undervalues and needs to be accounted for. With this method you can achieve what is called one standard deviation from the mean which is ___% variation of the score, while 2 standard deviation involves 95%. (10.02.2014, stats lec 4 variability)

68

7. For each of the following samples, determine the interval width that is most appropriate for a grouped frequency distribution and identify the approximate number of intervals needed to cover the range of scores. a. Sample scores range from X = 24 to X = 41 b. Sample scores range from X = 46 to X = 103 c. Sample scores range from X = 46 to X = 133

7. a. 2 points wide and around 8 intervals b. 5 points wide and around 12 intervals or 10 points wide and around 6 intervals c. 10 points wide and around 9 intervals

7. For a population with a standard deviation of a = 20, how large a sample is necessary to have a standard error that is: a. less than or equal to 5 points? b. less than or equal to 2 points? c. less than or equal to 1 point? (11.2.2014, stats ch 7, probability )

7. a. n ≥ 16 b. n ≥ 100 c. n ≥ 400

7. On an exam with a mean of M = 78, you obtain a score of X = 84. a. Would you prefer a standard deviation of s = 2 or s = 10? (Hint: Sketch each distribution and find the location of your score.) b. If your score were X = 72, would you prefer s = 2 or s = 10? Explain your answer. (10.03.2014 Stats ch 4 textbook extraction/notes)

7. a. s = 2 is better (you are above the mean by 3 standard deviations). b. s = 10 is better (you are below the mean by less than half a standard deviation).

8. What information can you obtain about the scores in a regular frequency distribution table that is not available from a grouped table?

8. A regular table reports the exact frequency for each category on the scale of measurement. After the categories have been grouped into class intervals, the table reports only the overall frequency for the interval but does not indicate how many scores are in each of the individual categories.

8. A population has a mean of p. = 30 and a standard deviation of if = 5. a. If 5 points were added to every score in the population, what would be the new values for the mean and standard deviation? b. If every score in the population were multiplied by 3 what would be the new values for the mean and standard deviation? (10.03.2014 Stats ch 4 textbook extraction/notes)

8. a. The mean is μ = 35 and the standard deviation is still σ = 5. b. The new mean is μ = 90 and the new standard deviation is σ = 15.

8. If the population standard deviation is a = 8, how large a sample is necessary to have a standard error that is: a. less than 4 points? b. less than 2 points? c. less than 1 point? (11.2.2014, stats ch 7, probability )

8. a. n > 4 b. n > 16 c. n > 64

9. Describe the difference in appearance between a bar graph and a histogram and describe the circumstances in which each type of graph is used.

9. A bar graph leaves a space between adjacent bars and is used with data from nominal or ordinal scales. In a histogram, adjacent bars touch at the real limits. Histograms are used to display data from interval or ratio scales.

9. a. After 3 points have been added to every score in a sample, the mean is found to be M = 83 and the standard deviation is s = 8. What were the values for the mean and standard deviation for the original sample? b. After every score in a sample has been multiplied by 4, the mean is found to be M = 48 and the standard deviation is s = 12. What were the values for the mean and standard deviation for the original sample? (10.03.2014 Stats ch 4 textbook extraction/notes)

9. a. The original mean is M = 80 and the standard deviation is s = 8. b. The original mean is M = 12 and the standard deviation is s = 3.

9. For a sample of n = 25 scores, what is the value of the population standard deviation (cr) necessary to produce each of the following a standard error values? a. um = 10 points? b. cr,w = 5 points? c. crAi = 2 points? (11.2.2014, stats ch 7, probability )

9. a. σ = 50 b. σ = 25 c. σ = 10

The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. In the situation of a sample you would subtract 1 from the number dividing for the mean of the squared numbers because of a concept called degrees of freedom which mainly is that there is a tendency for deviations to be undervalues and needs to be accounted for. With this method you can achieve what is called one standard deviation from the mean which is 68% variation of the score, while 2 standard deviation involves ___%. (10.02.2014, stats lec 4 variability)

95

What is a smooth curve? What does symmetrical shape mean? What is bimodal? What is a positive shew and a negative shew and how can you tell which direction it is? (stats lec 2)

A smooth curve a generationalization. Symmetrical is if graph divided in half it would be the same. It suggests no skew and a good data set. Bimodal is a double curve that is still symmentical. Positive shew has the tail going right. Negative tail going left.

10.25.2014, Stats ch 6 Probability and unit normal table) 1. For a normal distribution with a mean of p = 60 and a standard deviation of a = 12, find each probability value requested. a. p(X > 66) b. p(X < 75) c. p(X < 57) d. p(48 < X < 72) 2. Scores on the Mathematics section of the SAT Reasoning Test form a normal distribution with a mean of p = 500 and a standard deviation of a = 100. a. If the state college only accepts students who score in the top 60% on this test, what is the minimum score needed for admission? b. What is the minimum score necessary to be in the top 10% of the distribution? c. What scores form the boundaries for the middle 50% of the distribution? 3. What is the probability of selecting a score greater than 45 from a positively skewed distribution with p = 40 and a = 10? (Be careful.)

ANSWERS I. a. p = 0.3085 b. p = 0.8944 C. p = 0.4013 d. p = 0.6826 2. a. z = —0.25; X = 475 b. z = 1.28; X = 628 c. z = ±0.67; X =433 and X =567 3. You cannot obtain the answer. The unit normal table cannot be used to answer this question because the distribution is not normal.

What are bar graphs and pie graphs good for in regards to frequency data? What's the difference between a histogram and a pie graph? (stats lec 2)

Bar graphs and pie graphs are good for visualizing smaller sets of simple frequency data. Unlike hisograms bar graphs are not spaced together

10.25.2014, Stats ch 6 Probability and unit normal table) What proportion of the normal distribution corresponds to z-score values greater than z = 1.00?

First, you should sketch the distribution and shade in the area you are trying to determine. This is shown in Figure 6.8(a). In this case, the shaded portion is the tail of the distribution beyond z = 1.00. To find this shaded area, you simply look for z = 1.00 in column A to find the appropriate row in the unit normal table. Then scan across the row to column C (tail) to find the proportion. Using the table in Appendix B, you should find that the answer is 0.1587. You also should notice that this same problem could have been phrased as a probability question. Specifically, we could have asked, "For a normal distribution, what is the probability of selecting a z-score value greater than z = +1.00?" Again, the answer is p(z > 1.00) = 0.1587 (or 15.87%).

When is it best to use the mode?

If there there unspecific values, nominal values or discrete Can also contain major and minor modes

What is the interpolation? What's an example of this that the professor gave involving average snowfall? (stats lec 3)

Interpolation is essentially an assumption that change is constant that lets us guess at any point of the data. The example of snowfall is that if we know there will be for example 15 inches of snow fall this month then we can make the assumption that when half the month is over there will be 7.5 inches of snowfall

There are three forms of verifiability. The first is called the range difference .It is the simplest type but can be influenced by outliers or explain values which make it less useful. The second is the_____________ of 25th to 75th percentile. This is a better representation of the outliers, but may not give the entire picture of the variables. The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. (10.02.2014, stats lec 4 variability)

Interquartile range

Why is it important to check that the total of p=f/N row in normal frequency tables equals 1 and that the percentage table equals 100? (stats lec 2)

It's good to double check in case numbers are carried over incorrectly

In mean, medium, and mode what are best used for? (Stats Lec 3)

Mean is best used most of the time because it includes all the data sets and allows for multiple data points. The medium is best used when there is an extreme varient. And a mode is best used when there is an extreme and a large amount of data.

If a data set is highly skewed on the left but there are some distribution on the right what type of central tendency should be used?

Medium

If there is an open ended group like 5 or more people ate pizza what central tendency should be used?

Medium

In a study measuring time it takes for people to finish a test if someone never finishes what central tendency should be used?

Medium

What happens if you ad a new score to the distribution? What happens if the score is exactly the same as the mean?

New score will change the mean. If exactly the same though there will be no change.

What happens to the mean if you multiply every distribution by the same amount? What happens if you divide?

Nothing changes

Order of operations (People eat my ducks always seriously) (stats lec 2)

Parathisis Exponents Multiply Dividing Addition (Includes E Stigma) Subtration

What is polygon good for in regards to frequency tables? What does it look like on top of a histogram? (stats lec 2)

Polygons are another way to display group frequency data.

___________ equals the mean squared deviation. Variance is the average squared distance from the mean. While Standard deviation is the variance squared. (10.03.2014 Stats ch 4 textbook extraction/notes)

Population variance

What are real limits in context of group frequencies? Why are they important? What is the general rules to using real limits? What happens if the number falls on the limit?

Real limits is able to better capture complete continuous data. Set up boundaries of intervals on the half (0.5). If it falls on limit then you put it in the top portion.

What are regular frequency tables good for? How many rows are there and what is each row supposed to display? (XFFP - Xenophobes fight factions periodically) (stats lec 2)

Regular frequency tables are better for displaying small sets of data. The rows display x, frequency, fraction - decimal p=f/N (N is total number) Percentage

A population forms a normal distribution with a mean of p = 60 and a standard deviation of a = 12. For a sample of n = 36 scores from this population, what is the probability of obtaining a sample mean greater than 64? p(M > 64) = ? (11.2.2014, stats ch 7, probability )

STEP 1 Rephrase the probability question as a proportion question. Out of all of the possible sample means for n = 36, what proportion has values greater than 64? All of the possible sample means is simply the distribution of sample means, which is normal, with a mean of p = 60 and a standard error of a 12 12 0-m = VW .\/ 6 = = =2 The distribution is shown in Figure 7.13(a). Because the problem is asking for the proportion greater than M = 64, this portion of the distribution is shaded in Figure 7.13(b). STEP 2 Compute the z-score for the sample mean. to a z-score of M — 64 — 60 4 z= = =2.00 QM 2 2 Therefore, p(M > 64) = p(z > 2.00) A sample mean of M = 64 corresponds STEP 3 Look up the proportion in the unit normal table. Find z = 2.00 in column read across the row to find p = 0.0228 in column C. This is the answer as shown Figure 7.13(c). p(M > 64) = p(z> 2.00) = 0.0228 (or 2.28%)

Population variance equals the mean squared deviation. Variance is the average squared distance from the mean. While ___________ is the variance squared. (10.03.2014 Stats ch 4 textbook extraction/notes)

Standard deviation

10.25.2014, Stats ch 6 Probability and unit normal table) Many problems require that you find proportions for negative z-scores. For example, what proportion of the normal distribution is contained in the tail beyond z = —0.50?

That is, p(z < —0.50). This portion has been shaded in Figure 6.8(c). To answer questions with negative z-scores, simply remember that the normal distribution is symmetrical with a z-score of zero at the mean, positive values to the right, and negative values to the left. The proportion in the left tail beyond z = —0.50 is identical to the proportion in the right tail beyond z = +0.50. To find this proportion, look up z = 0.50 in column A, and read across the row to find the proportion in column C (tail). You should get an answer of 0.3085 (30.85%).

What does E Stimga mean? What does Ex mean? (stats lec 2)

This notation means the sum of all. This notation next to x means the sum of x values

What are frequency distributions good for? What are the two types of frequency tables? (stats lec 2)

This type of distribution technique is good for organizing and simplifying data. The two types of frequency tables are regular frequency tables and group frequency table.

_________ measures how well an individual score (or group of scores) represents the entire distribution. This aspect is very important for inferential statistics, in which relatively small samples are used to answer questions about populations. For example, suppose that you selected a sample of one person to represent the entire population. Because most adult males have heights that are within a few inches of the population average (the distances are small), there is a very good chance that you would select someone whose height is within 6 inches of the population mean. On the other hand, the scores are much more spread out (greater distances) in the distribution of weights. In this case, you probably would not obtain someone whose weight was within 6 pounds of the population mean. Thus, it provides information about how much error to expect if you are using a sample to represent a population (10.03.2014 Stats ch 4 textbook extraction/notes, var)

Variability

___________ provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. (10.03.2014 Stats ch 4 textbook extraction/notes)

Variability

When should you use group frequency distribution? What are the 4 rules which you have to remember to follow? (TWBS Those wet bitches suck)

You should use group frequency distribution when there is a lot of numbers or when the number is more complex and continuous. The 4 rules are Ten sections Width of interval to be simple Bottom scores shares a multiple with the width Sum of width complete range stores

The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. In the situation of ________ you would subtract 1 from the number dividing for the mean of the squared numbers because of a concept called degrees of freedom which mainly is that there is a tendency for deviations to be undervalues and needs to be accounted for. With this method you can achieve what is called one standard deviation from the mean which is 68% of the score, while 2 standard deviation involves 95%. (10.02.2014, stats lec 4 variability)

a sample

10.25.2014, Stats ch 6 Probability and unit normal table) The first column (A) lists z-score values corresponding to ____a___. If you imagine a vertical line drawn through a normal distribution, then the exact location of the line can be described by one of the z-score values listed in column A. You should also realize that a vertical line separates the distribution into two sections: a larger section called the body and a smaller section called the tail. ___b___ in the table identify the proportion of the distribution in each of the two sections. Column B presents ___c___, and column C presents the proportion ___d___. Finally, we have added a fourth column, column D, that ____e_____. We use the distribution To make full use of the unit normal table, there are a few facts to keep in mind: 1. The body always corresponds to the ___f___ part of the distribution whether it is on the right-hand side or the left-hand side. Similarly, the tail is always the smaller section whether it is on the right or the left. 2. Because the normal distribution is ___g___, the proportions on the righthand side are exactly the same as the corresponding proportions on the lefthand side. 3. Although the z-score values change signs (+ and —) from one side to the other, the proportions are always ___h___. Thus, column C in the table always lists the proportion in the tail whether it is the right-hand tail or the left-hand tail.

a. different positions in a normal distribution b. Columns B and C c. the proportion in the body (the larger portion) d. in the tail e. identifies the proportion of the distribution that is located between the mean and the z-score f. larger g. symmetrical h. positive

(Stats ch 5) Z-scores take the standard deviation and each x value into a standard score. It is useful because ___a___. In addition it allows z-scores from one standard to be compared ____b___. () The ___c___ tells you whether the score is located below or above the mean. The number tells you the ____d____. () the z score formula is z = (x-u)/o. The numerator is a deviation score which is divided by o because _____e_____. While the formula for a sample is z = (X-M)/s, x is sample score, M is the sample mean, s is standard deviation. ()()()if given standard deviation, mean, and zscore you can calculate X but multiplying the zscore by the standard deviation and then adding it to the mean or simply using this formula ____e___. ()()()for zscores the mean should always have a mean of 0 _____f___. The shape of graphs should not be changed by zscore, but the value of the mean will become 0. ()()() A standard distribution is composed of scores that have _____g____. This way two different distributions can be compared, for example the score of two separate classes. This is done by simple multiplying z score to standard deviation. The same can work for a ___h___ but we must remember that it is a sample standard distribution. ()()() To find the sum of distribution of z score you_____i____. ()()()Z Scores can be used to interpret whether a certain type of treatment caused a major difference. If for example the a rat injected with a growth hormone grows zscore=+4 then we see that there was a ___j___.

a. it tells the exact location of the original X value within the distribution b. to another standard like for example IQ c. sign (+) or (-) d. distance between the score and mean in terms of the number of standard deviations e. we want the z score to measure in terms of standard deviation f. because it's values should all be either above or below the mean g. been transformed to create predetermined values fod u and o h. sample i. go through the same process of squaring the numbers j. big difference between normal controls and the rats that got a better standard

4. Find each value requested for the distribution of scores in the following table. a. n b. EX c. Ex^2 Frequency table X: 5 4 3 2 1 f: 1 2 3 5 3

a. n=14 b. EX = 35 c. 107

(Stats ch 5) ___a___ take the ___b____. It is useful because it tells the exact location of the original X value within the distribution. In addition it allows z-scores from one standard to be compared to another standard like for example IQ. () The sign (+) or (-) tells you whether ____c____. The number tells you the distance between the score and mean in teems of the number of standard deviations. () the z score formula is ____d____ . The numerator is a deviation score which is divided by o because we want the z score to measure in terms of standard deviation. While the formula for a sample is z = (X-M)/s, x is sample score, M is the sample mean, s is standard deviation. ()()()if given standard deviation, mean, and zscore you can calculate X by ____e___ or simply using this formula x= u + zo. ()()()for zscores the mean should always have a mean of __f__ because it's values should all be either above or below the mean. The shape of graphs should not be changed by zscore, but the value of the mean will become 0. ()()() A ___g___ is composed of scores that have been transformed to create predetermined values for u and o. This way two different distributions can be compared, for example the score of two separate classes. This is done by simple multiplying z score to standard deviation. The same can work for a sample but we must remember that ____h___. ()()() To find the sum of ___i___ of z score you go through the same process of squaring the numbers. ()()()Z Scores can be used to interpret whether a certain type of treatment caused a ___j___. If for example the a rat injected with a growth hormone grows zscore=+4 then we see that there was a big difference

a. zscores b. standard deviation and each x value into a standard score c. the score is located below or above the mean d. z = (x-u)/o e. multiplying the zscore by the standard deviation and then adding it to the mean f. 0 g. standard distribution h. it is a sample standard distribution i. distribution j. major difference

Variability describes the distribution. Specifically, it tells whether the scores ________________________. Usually, variability is defined in terms of distance. It tells how much distance to expect between one score and another, or how much distance to expect between an individual score and the mean. For example, we know that the heights for most adult males are clustered close together, within 5 or 6 inches of the average. Although more extreme heights exist, they are relatively rare. (10.03.2014 Stats ch 4 textbook extraction/notes)

are clustered close together or are spread out over a large distance

Variability measures how well an individual score (or group of scores) represents the entire distribution. This aspect of variability is very important for inferential statistics, in which relatively small samples are used to answer questions about populations. For example, suppose that you selected a sample of one person to represent the entire population. Because most adult males have heights that are within a few inches of the population average (the distances are small), there is a very good chance that you would select someone whose height is within 6 inches of the population mean. On the other hand, the scores ______________in the distribution of weights. In this case, you probably would not obtain someone whose weight was within 6 pounds of the population mean. Thus, variability provides information about how much error to expect if you are using a sample to represent a population (10.03.2014 Stats ch 4 textbook extraction/notes)

are much more spread out (greater distances)

Variability measures how well an individual score (or group of scores) represents the entire distribution. This aspect of variability is very important for inferential statistics, in which relatively small samples _____________. For example, suppose that you selected a sample of one person to represent the entire population. Because most adult males have heights that are within a few inches of the population average (the distances are small), there is a very good chance that you would select someone whose height is within 6 inches of the population mean. On the other hand, the scores are much more spread out (greater distances) in the distribution of weights. In this case, you probably would not obtain someone whose weight was within 6 pounds of the population mean. Thus, variability provides information about how much error to expect if you are using a sample to represent a population (10.03.2014 Stats ch 4 textbook extraction/notes)

are used to answer questions about populations

Though central tendencies tell us good information, it is missing deacriptions of how many people are close to the average or whether they are scattered throughout the scores. Measures of variability therefore is used to find how variable terms alongside _______ statistics such as mean, medium, or mode. (10.02.2014, stats lec 4 variability)

basic descriptive statistics

A sample statistic is unbiased if the average value of the statistic is equal to the population parameter. (The average value of the statistic is obtained from all the possible samples for a specific sample size, n.) A sample statistic is __________ if the average value of the statistic either underestimates or overestimates the corresponding population parameter. (10.03.2014 Stats ch 4 textbook extraction/notes)

biased

There are three forms of verifiability. The first is called the range difference .It is the simplest type but can be influenced __________________________. The second is the Interquartile range of 25th to 75th percentile. This is a better representation of the outliers, but may not give the entire picture of the variables. The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. (10.02.2014, stats lec 4 variability)

by outliers or explain values which make it less useful

The standard deviation is the most commonly used and the most important measure of variability. Standard deviation uses the mean of the distribution as a reference point and measures variability by considering the distance between each score and the mean. In simple terms, the standard deviation provides a measure of the standard, or average, distance from the mean, and describes whether the scores are _______________. (10.03.2014 Stats ch 4 textbook extraction/notes)

clustered closely around the mean or are widely scattered

The range is probably the most obvious way to describe how spread out the scores are—simply find the distance between the maximum and the minimum scores. The problem with using the range as a measure of variability is that it is _________________. Thus, a distribution with one unusually large (or small) score has a large range even if the other scores are all clustered close together. (10.03.2014 Stats ch 4 textbook extraction/notes)

completely determined by the two extreme values and ignores the other scores in the distribution

The standard deviation is the most commonly used and the most important measure of variability. Standard measures variability by _____________. In simple terms, the standard deviation provides a measure of the standard, or average, distance from the mean, and describes whether the scores are clustered closely around the mean or are widely scattered. (10.03.2014 Stats ch 4 textbook extraction/notes)

considering the distance between each score and the mean

Deviation from the mean is the ____________. It measures the deviation from a common central tendency. It can tell us how an individual stands in relation to the other scores as well us how accurate this set of scores is to a population. When there is a small vulnerability then it is a good representation because it means that more scores are contained in an area. (10.02.2014, stats lec 4 variability)

conventional form of variation

The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. In the situation of a sample you would subtract 1 from the number dividing for the mean of the squared numbers because of a concept called ______________ which mainly is that there is a tendency for deviations to be undervalues and needs to be accounted for. With this method you can achieve what is called one standard deviation from the mean which is 68% of the score, while 2 standard deviation involves 95%. (10.02.2014, stats lec 4 variability)

degrees of freedom

Variability provides a quantitative measure of the ______________ in a distribution and describes the degree to which the scores are spread out or clustered together. (10.03.2014 Stats ch 4 textbook extraction/notes)

differences between scores

The third is or called the standard variation which is the average squared distance from the mean. This involves finding the _____________, square each distance, find the average of the result and then square rooting it. In the situation of a sample you would subtract 1 from the number dividing for the mean of the squared numbers because of a concept called degrees of freedom which mainly is that there is a tendency for deviations to be undervalues and needs to be accounted for. With this method you can achieve what is called one standard deviation from the mean which is 68% of the score, while 2 standard deviation involves 95%. (10.02.2014, stats lec 4 variability)

distance of each integer of the mean

There are three forms of verifiability. The first is called the range difference .It is the simplest type but can be influenced by outliers or explain values which make it less useful. The second is the Interquartile range of 25th to 75th percentile. This is a better representation of the outliers, but may not give the _______________. The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. (10.02.2014, stats lec 4 variability)

entire picture of the variables

A sample statistic is unbiased if the average value of the statistic is _________. (The average value of the statistic is obtained from all the possible samples for a specific sample size, n.) A sample statistic is biased if the average value of the statistic either underestimates or overestimates the corresponding population parameter. (10.03.2014 Stats ch 4 textbook extraction/notes)

equal to the population parameter

Variability measures how well an individual score (or group of scores) represents the entire distribution. This aspect of variability is very important for inferential statistics, in which relatively small samples are used to answer questions about populations. For example, suppose that you selected a sample of one person to represent the entire population. Because most adult males have heights that are within a few inches of the population average (the distances are small), there is a very good chance that you would select someone whose height is within 6 inches of the population mean. On the other hand, the scores are much more spread out (greater distances) in the distribution of weights. In this case, you probably would not obtain someone whose weight was within 6 pounds of the population mean. Thus, variability provides information about how much _________ to expect if you are using a sample to represent a population (10.03.2014 Stats ch 4 textbook extraction/notes)

error

The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, _____________ and then square rooting it. In the situation of a sample you would subtract 1 from the number dividing for the mean of the squared numbers because of a concept called degrees of freedom which mainly is that there is a tendency for deviations to be undervalues and needs to be accounted for. With this method you can achieve what is called one standard deviation from the mean which is 68% of the score, while 2 standard deviation involves 95%. (10.02.2014, stats lec 4 variability)

find the average of the result

Though central tendencies tell us good information, it is missing deacriptions of ____________. Measures of variability therefore is used to find how variable terms alongside basic descriptive statistics such as mean, medium, or mode. (10.02.2014, stats lec 4 variability)

how many people are close to the average or whether they are scattered throughout the scores

When you add a constant number to the variables the mean changes but the standard deviation does not change. On the other hand if you multiply by a constant then the standard deviation will ______________. (10.02.2014, stats lec 4 variability)

increase by that change multiple

Deviation from the mean is the conventional form of variation. It measures the deviation from a common central tendency. It can tell us how an ________________ as well us how accurate this set of scores is to a population. When there is a small vulnerability then it is a good representation because it means that more scores are contained in an area. (10.02.2014, stats lec 4 variability)

individual stands in relation to the other scores

Deviation from the mean is the conventional form of variation. It measures the deviation from a common central tendency. It can tell us how an individual stands in relation to the other scores as well as how accurate this set of scores is to a population. When there is a small vulnerability then it is a good representation because _________________ (10.02.2014, stats lec 4 variability)

it means that more scores are contained in an area.

The range is probably the most obvious way to describe how spread out the scores are—simply find the distance between the maximum and the minimum scores. The problem with using the range as a measure of variability is that it is completely determined by the two extreme values and ignores the other scores in the distribution. Thus, a distribution with one unusually large (or small) score has a _______ range even if the other scores are all clustered close together. (10.03.2014 Stats ch 4 textbook extraction/notes)

large

The second is the Interquartile range of 25th to 75th percentile. This is a better representation of the outliers, but may not give the entire picture of the variables. To achieve this you look for the the second quarter of the value. The general idea is (3rd quarter) - (1st quarter). A semi interqualtile range is the ________________ which is defined by the middle 50%. (10.02.2014, stats lec 4 variability)

middle of distribution to the boundary

When you add a constant number to the variables the mean changes but the standard deviation does not change. On the other hand if you _________ constant then the standard deviation will increase by that change multiple. (10.02.2014, stats lec 4 variability)

multiply by a

10.25.2014, Stats ch 6 Probability and unit normal table) For a normal distribution, what z-score separates the top 10% from the remainder of the distribution? To answer this question, we have sketched a normal distribution [Figure 6.9(a)] and drawn a vertical line that separates the highest 10% (approximately) from the rest. The problem is to locate the exact position of this line. For this distribution, we know that the tail contains 0.1000 (10%) and the body contains 0.9000 (90%). To find the z-score value, you simply

ocate the row in the unit normal table that has 0.1000 in column C or 0.9000 in column B. For example, you can scan down the values in column C (tail) until you find a proportion of 0.1000. Note that you probably will not find the exact proportion, but you can use the closest value listed in the table. For this example, a proportion of 0.1000 is not listed in column C but you can use 0.1003, which is listed. Once you have found the correct proportion in the table, simply read across the row to find the corresponding z-score value in column A. For this example, the z-score that separates the extreme 10% in the tail is z = 1.28. At this point you must be careful because the table does not differentiate between the right-hand tail and the left-hand tail of the distribution. Specifically, the final answer could be either z = +1.28, which separates 10% in the right-hand tail, or z = —1.28, which separates 10% in the left-hand tail. For this problem we want the right-hand tail (the highest 10%), so the z-score value is z = +1.28. EXAMPLE 6 . 4 B For a normal distribution, what z-score values form the boundaries that separate the middle 60% of the distribution from the rest of the scores? Again, we have sketched a normal distribution [Figure 6.9(b)] and drawn vertical lines so that roughly 60% of the distribution in the central section, with the remainder

The _______ is probably the most obvious way to describe how spread out the scores are—simply find the distance between the maximum and the minimum scores. The problem with using the range as a measure of variability is that it is completely determined by the two extreme values and ignores the other scores in the distribution. Thus, a distribution with one unusually large (or small) score has a large range even if the other scores are all clustered close together. (10.03.2014 Stats ch 4 textbook extraction/notes)

range

There are three forms of verifiability. The first is called the ___________ It is the simplest type and can be influenced by outliers or explain values which make it less useful. The second is the Interquartile range of 25th to 75th percentile. This is a better representation of the outliers, but may not give the entire picture of the variables. The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. (10.02.2014, stats lec 4 variability)

range difference.

Variability provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the _______________. (10.03.2014 Stats ch 4 textbook extraction/notes)

scores are spread out or clustered together

The second is the Interquartile range of 25th to 75th percentile. This is a better representation of the outliers, but may not give the entire picture of the variables. To achieve this you look for the the_______________. The general idea is (3rd quarter) - (1st quarter). A semi interqualtile range is the middle of distribution to the boundary which is defined by the middle 50%. (10.02.2014, stats lec 4 variability)

second quarter of the value

The second is the Interquartile range of 25th to 75th percentile. This is a better representation of the outliers, but may not give the entire picture of the variables. To achieve this you look for the the second quarter of the value. The general idea is (3rd quarter) - (1st quarter). A__________ range is the middle of distribution to the boundary which is defined by the middle 50%. (10.02.2014, stats lec 4 variability)

semi interqualtile

Deviation from the mean is the conventional form of variation. It measures the deviation from a common central tendency. It can tell us how an individual stands in relation to the other scores as well as how accurate this set of scores is to a population. When there is a _____________ then it is a good representation because it means that more scores are contained in an area. (10.02.2014, stats lec 4 variability)

small vulnerability

The range is probably the most obvious way to describe how _________ the scoresare—simply find the distance between the maximum and the minimum scores. The problem with using the range as a measure of variability is that it is completely determined by the two extreme values and ignores the other scores in the distribution. Thus, a distribution with one unusually large (or small) score has a large range even if the other scores are all clustered close together. (10.03.2014 Stats ch 4 textbook extraction/notes)

spread out

The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, _____________, find the average of the result and then square rooting it. In the situation of a sample you would subtract 1 from the number dividing for the mean of the squared numbers because of a concept called degrees of freedom which mainly is that there is a tendency for deviations to be undervalues and needs to be accounted for. With this method you can achieve what is called one standard deviation from the mean which is 68% of the score, while 2 standard deviation involves 95%. (10.02.2014, stats lec 4 variability)

square each distance

The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then _____________. In the situation of a sample you would subtract 1 from the number dividing for the mean of the squared numbers because of a concept called degrees of freedom which mainly is that there is a tendency for deviations to be undervalues and needs to be accounted for. With this method you can achieve what is called one standard deviation from the mean which is 68% of the score, while 2 standard deviation involves 95%. (10.02.2014, stats lec 4 variability)

square rooting it

The _________ is the most commonly used and the most important measure of variability. Standard deviation uses the mean of the distribution as a reference point and measures variability by considering the distance between each score and the mean. In simple terms, the standard deviation provides a measure of the standard, or average, distance from the mean, and describes whether the scores are clustered closely around the mean or are widely scattered. (10.03.2014 Stats ch 4 textbook extraction/notes)

standard deviation

There are three forms of verifiability. The first is called the range difference .It is the simplest type but can be influenced by outliers or explain values which make it less useful. The second is the Interquartile range of 25th to 75th percentile. This is a better representation of the outliers, but may not give the entire picture of the variables. The third is or called the __________ which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. (10.02.2014, stats lec 4 variability)

standard variation

The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. In the situation of a sample you would _______________________ because of a concept called degrees of freedom which mainly is that there is a tendency for deviations to be undervalues and needs to be accounted for. With this method you can achieve what is called one standard deviation from the mean which is 68% of the score, while 2 standard deviation involves 95%. (10.02.2014, stats lec 4 variability)

subtract 1 from the number dividing for the mean of the squared numbers

Variability measures how well an individual score (or group of scores) represents ________. This aspect is very important for inferential statistics, in which relatively small samples are used to answer questions about populations. For example, suppose that you selected a sample of one person to represent the entire population. Because most adult males have heights that are within a few inches of the population average (the distances are small), there is a very good chance that you would select someone whose height is within 6 inches of the population mean. On the other hand, the scores are much more spread out (greater distances) in the distribution of weights. In this case, you probably would not obtain someone whose weight was within 6 pounds of the population mean. Thus, variability provides information about how much error to expect if you are using a sample to represent a population (10.03.2014 Stats ch 4 textbook extraction/notes)

the entire distribution

Variability describes the distribution. Specifically, it tells whether the scores are clustered close together or are spread out over a large distance. Usually, variability is defined in terms of distance. It tells how much distance to expect between one score and another, or how much distance to expect between an individual score and___________. For example, we know that the heights for most adult males are clustered close together, within 5 or 6 inches of the average. Although more extreme heights exist, they are relatively rare. (10.03.2014 Stats ch 4 textbook extraction/notes)

the mean

Population variance equals_____________. Variance is the average squared distance from the mean. While Standard deviation is the variance squared. (10.03.2014 Stats ch 4 textbook extraction/notes)

the mean squared deviation

Deviation from the mean is the conventional form of variation. It measures the deviation from a common central tendency. It can tell us how an individual stands in relation to the other scores as well as how accurate this set of scores is ____________. When there is a small vulnerability then it is a good representation because it means that more scores are contained in an area. (10.02.2014, stats lec 4 variability)

to a population

A sample statistic is _______ if the average value of the statistic is equal to the population parameter. (The average value of the statistic is obtained from all the possible samples for a specific sample size, n.) A sample statistic is biased if the average value of the statistic either underestimates or overestimates the corresponding population parameter. (10.03.2014 Stats ch 4 textbook extraction/notes)

unbiased

A sample statistic is unbiased if the average value of the statistic is equal to the population parameter. (The average value of the statistic is obtained from all the possible samples for a specific sample size, n.) A sample statistic is biased if the average value of the statistic either ____________ the corresponding population parameter. (10.03.2014 Stats ch 4 textbook extraction/notes)

underestimates or overestimates

The third is or called the standard variation which is the average squared distance from the mean. This involves finding the distance of each integer of the mean, square each distance, find the average of the result and then square rooting it. In the situation of a sample you would subtract 1 from the number dividing for the mean of the squared numbers because of a concept called degrees of freedom which mainly is that there is a tendency for deviations to be __________________. With this method you can achieve what is called one standard deviation from the mean which is 68% of the score, while 2 standard deviation involves 95%. (10.02.2014, stats lec 4 variability)

undervalues and needs to be accounted for

10.25.2014, Stats ch 6 Probability and unit normal table) For a normal distribution, what is the probability of selecting a z-score less than z = 1.50? In symbols, p(z < 1.50) = ?

ur goal is to determine what proportion of the normal distribution corresponds to z-scores less than 1.50. A normal distribution is shown in Figure 6.8(b) and z = 1.50 is marked in the distribution. Notice that we have shaded all the values to the left of (less than) z = 1.50. This is the portion we are trying to find. Clearly the shaded portion is more than 50%, so it corresponds to the body of the distribution. Therefore, find z = 1.50 in column A of the unit normal table and read across the row to obtain the proportion from column B. The answer is p(z < 1.50) = 0.9332 (or 93.32%).

Though central tendencies tell us good information, it is missing deacriptions of how many people are close to the average or whether they are scattered throughout the scores. Measures of ________ therefore is used to find how variable terms alongside basic descriptive statistics such as mean, medium, or mode. (10.02.2014, stats lec 4 variability)

variability

Population variance equals the mean squared deviation. Variance is the average squared distance from the mean. While Standard deviation is the _________. (10.03.2014 Stats ch 4 textbook extraction/notes)

variance squared

Deviation is distance from the mean: deviation score = X - u. What is x? What is u? (10.03.2014 Stats ch 4 textbook extraction/notes)

x is the integer while u is the deviation from the mean