Intro to STATS CH Questions & HW

How many scores in the distribution are used to compute the range? a) only 1 b) 2 c) 50% d) all of the scores

2

What is the range for the following sets of scores? 3, 7, 9, 10, 12

9 or 10

A research study comparing alcohol use for college students in the US and Canada reports that more Canadian students drink but American students drink more. What research design did this study use? A) Correlational B) Experimental C) Non-experimental D) Non-correlational

C) Non-experimental

Statistical techniques that summarize, organize, and simplify data are classified as __________________. A) Population Statistics B) Sample Statistics C) Descriptive Statistics D) Inferential Statistics

C) Descriptive Statistics

An operational definition is used to ________________ a hypothetical construct. A) Define B) Measure C) Measure and define D) None of the other choices is correct

C) Measure and define

A researcher is curious about the average IQ of registered voters in the state of Florida. The entire group of registered voters in the stat is an example of ___________________? A) Sample B) Statistic C) Population D) Parameter

C) Population

Calculate the 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)

SS = 28 Variance = 4 Standard Deviation = 2

Find the mean, median, and mode for the scores in the following frequency distribution table: X . f 8 . 1 7 . 1 6 . 2 5 . 5 4 . 2 3 . 2

The mean (average) is 66/13 = 5.08, the median (middle number) is 5, and the mode (most frequent) is 5.

In general, ___________________ statistical techniques are used to summarize the data from a research study and ________________ statistical techniques are used to determine what conclusions are justified by the results. A)Inferential, Descriptive B)Descriptive, Inferential C)Sample, Population D)Population, Sample

B) Descriptive, Inferential

A researcher is interested in the sleeping habits of American college students. A group of 50 students are interviewed and the researcher finds that these students sleep an average of 6.7 hours per day. For this study, the average of 6.7 hours is an example of a (n) A) Parameter B) Statistic C) Population D) Sample

B) Statistic

In a correlational study, how many variables are measured for each individual and how many groups of scores are obtained? A) 1 variable and 1 group B) 1 Variable and 2 groups C) 2 Variable and 1 group D) 2 Variable and 2 groups

C) 2 Variables and 1 group

A population of N=15 scores has SUMX=120. What is the population mean?

µ = 120/15 = 8

Schmidt measured the # of each type of sentence recalled by each participant. The following scores are similar to the results obtained in the study. Humorous Non-Humorous 4 5 2 4 5 2 4 2 6 7 6 6 2 3 1 6 2 5 4 3 3 2 3 3 1 3 5 5 4 1 5 3 Calculate the mean number of sentences recalled for each of the two conditions. Do the data suggest that humor helps memory?

-The participants recalled an average of M = 68/16 = 4.25 humorous sentences compared to M = 49/16 = 3.06 non-humorous sentences. Humor does appear to improve memory performance.

The results of a recent study showed that children who routinely drank reduced fat milk (1% or skim) were more likely to be overweight or obese at age 2 and 4 compared to children who drank whole or 2% milk. Is this an example of an experimental or a non-experimental study?

-This is not an experiment because no independent variable is manipulated. The researchers are comparing two preexisting groups of individuals consisting of children who are already drinking whole milk or 2% milk. This design would be referred to as a quasi-experimental

Explain why the median is often preferred to the mean as a measure of central tendency doe a skewed distribution?

-With a skewed distribution, the extreme scores in the tail can displace the mean out toward the tail. The result is that the mean is often not a very representative value.

What is the variance for the following set of scores? 2, 2, 2, 2, 2, 2 a) 0 b) 2 c) 4 d) 5

0

Which of the following values is the most reasonable estimate of the standard deviation for the set of scores in the following distribution? X . f 5 1 4 2 3 4 2 2 1 1 a) 0 b) 1 c) 3 d) 5

1

In a sample distribution, X=56 corresponds to z=1.00, and x=47 corresponds to z= -0.50. Find the mean and standard deviation for the sample.

: The distance between the two scores, 9 points, corresponds to 1.5 standard deviations by the definition of z-score. Each z-score jump, for example, from 1 to 2, represents a change of 1 standard deviation. Therefore, the standard deviation for this sample distribution is 6 since 1.5s = 9. Then, you can calculate the mean with the formula; M = X - (z * s) = 56 - (1)(6) = 50

Is it possible to obtain a negative value for the variance or the standard deviation?

: variance and standard deviation cannot be less than zero because they are computed by adding squared deviations. Squared deviations are always greater than or equal to zero

A researcher studies the factors the determine the # of children that couples decide to have. The variable, # of children, is an example of a ______________________ variable?

A) Discrete

The teacher in a communications class asks students to identify their favorite reality television show. The different television shows make up a ________ scale of measurement. A) Nominal B) Ordinal C) Interval D) Ration

A) Normial

When measuring height to the nearest half inch, what are the real limits for a score?

D) 67.75 & 68.25

IQ tests are standardized so that the average score is 100 for the entire group of people who take the test each year. However, if you selected a group of 20 people who took the test and computed their average IQ score you probably would not get 100. What statistical concept explains the differences between your mean and the mean for the entire group? A) Statistical Error B) Inferential Error C) Descriptive Error D) Sampling Error

D) Sampling Error

Stephens, Atkins, and Kingston found that participants were able to tolerate more pain when they shouted their favorite swear words over and over than when they shouted neutral words. For this study, what is the independent variable? A) The amount of pain tolerated B) The participants who shouted swear words C) The participants who shouted neutral words D) The kind of word shouted by the participants

D) The kind of word shouted by the participants

The following scores are the ages for a random sample of n=30 drivers who were issued speeding tickets in New York during 2008. Determine the best interval width and place the scores in a grouped frequency distribution table. From looking at your table, does it appear that tickets ate issued Equally across age groups? 17, 30, 45, 20, 39, 53, 28, 19, 24, 21, 34, 38, 22, 29, 64, 22, 44, 36, 16, 56, 20, 23, 58, 32, 25, 28, 22, 51, 26, 43

Lowest value = 16. Highest value = 64. Number of values needed in a frequency table: (64-16) + 1 = 49 Trial and Error: 49/5 = 9.8. Since you want 10 intervals, use a width = 5. The bottom number of each interval should be a multiple of 5. X f 60-64 . 1 55-59 . 2 50-54 2 45-49 1 Younger drivers, especially those 20 to 29 40-44 . 2 years old, tend to get more tickets. 35-39 3 30-34 3 25-29 5 20-24 8 15-19 3

What value is represented by the lowercase letter (n)?

The # of scores in a sample

What information is provided by the sign (+/-) of a z score? What information i provided by the numerical value of the z score?

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.

Which of the following sets of scores has the greatest variability? a) 2,3,7,12 b) 12, 15, 16, 17, c) 24,25,26,27 d) 42, 44, 45, 46

a) 2,3,7, 12

One sample has a mean of M=8 and a second sample has a mean of M=16. The two samples are combined into a single set of scores. a) What is the mean for the combined set if both of the original samples have n=4 scores? b) What is the mean for the combined set if the first sample has n=3 and the second sample has n=5 c) What is the mean for the combined set if the first sample has n=5 and the second sample has n=3?

a) The combined sample mean is M = 12. If 8 = ∑ , then ∑ = 32 If 16 = ∑ , then ∑ = 64 = 12 b) The combined sample mean is (24 + 80)/8 = 13. If 8 = ∑ , then ∑ = 24 If 16 = ∑ , then ∑ = 80 = 13 c) The combined sample mean is (40 + 48)/8 = 11. If 8 = ∑ , then ∑ = 40 If 16 = ∑ , then ∑ = 48 = 11 Notice how the average is in the middle of 8 and 16 when the sample sizes are equal. Otherwise, the combined average is closer to the value with the larger sample sizes

a) After 6 points have been added to every score in a sample, the mean is found to be M=70 and the standard deviation is s=13. What were the values for the mean and standard deviation for the original sample? b) After every score in a sample is multiplied by 3, the mean is found to be M=48 and the standard deviation is s=18. What were the values for the mean and standard deviation for the original sample?

a) The original mean M=64 and the standard deviation is s=13 b) The original mean is M=16 and the standard deviation is s=6

For the following population of N = 6 scores: 2, 9, 6, 8, 9, 8 a) Calculate the range and the standard deviation. (use either definition for the range) b) Add 2 points to each score and compute the range and standard deviation again. Describe how adding a constant to each score influences measure of variability

a) The range is 7 (discrete) or 8 points (continuous) and with SS = 36 the standard deviation is σ = √6 = 2.45. b) After adding 2 points, the range is still 7 or 8 and the standard deviation is still σ = 2.45.

If the sample variance is computed by dividing by n, instead of n-1, how will the obtained values be related to the corresponding population variance? a) They will consistently underestimate the population variance b) They will consistently overestimate the population variance c) The average value will be exactly equal to the population variance d) The average value will be close , but not exactly equal to, the population variance

a) They will consistently underestimate the population variance

Use summation notation to express each of the following calculations: a) Add the scores and then add then square the sum b) Square each score and then add the squared values c) subtract 2 points for each score and then add the resulting values d) Subtract 1 point from each score and square the resulting values. Then add the squared values.

a. (ΣX)2 b. ΣX2 c. Σ(X - 2) d. Σ(X - 1)2

Find each value requested for the distribution of scores in the following table: X . f 6 . 1 5 . 2 4 . 2 3 . 4 2 . 3 1 . 2 a) n b) SUM X c) SUM X^2

a. Add up all the values in the frequency (f) column to get the total sample size. n = 14 b. Add up all the values of your responses. Multiply each value of X with its frequency. ΣX = 6*1 + 5*2 + 4*2 + 3*4 + 2*3 + 1*2 = 44 c. Square each value of X and then multiply the square value by the frequency for that value. ΣX 2 = 168

Wegesin and Stern found greater consistency 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 variance for the scores for each woman b) Are the scores for the younger woman more consistent (less variable)

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.

The following table shoes four rows from a frequency distribution table for a sample of n=20 scores. Use interpolation to find the percentiles and percentile ranks requested: X . f . cf . c% 40-49 . 4 . 20 . 100 30-39 . 7 . 16 . 80 20-29 . 4 . 9 . 45 10-19 . 3 . 5 . 25 a) Find the 30th percentile? b) Find the 52nd percentile? c) What is the percentile rank for X=46? d) What is the percentile rank for X=21?

a. Score = 22 Cumul. %.: 25% 30% 45% Real U.L. : 19.5 ??? 29.5 Score=Y = 19.5 + (..) (. .) × (29.5-19.5) = 22 b. Score = 31.5 Cumul. %.: 45% 52% 80% Real U.L. : 29.5 ??? 39.5 Score = Y = 29.5 + (.. ) (.. ) × (39.5-29.5) = 31.5 c. Percentile Rank = 93% Cumul. %.: 80% ??? 100% Real U.L. : 39.5 46 49.5 Percentile Rank = Y = .80 + ( .) ( ..) × (1.00-.80) = .93 d. Percentile Rank = 28% Cumul. %.: 25% ??? 45% Real U.L. : 19.5 21 29.5 Percentile Rank = Y = .25 + (.) (..) × (.45-.25)= 0.8

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?

a. The definitional formula works well when the mean is a whole number and there is a relatively small number of scores. b. The computational formula is better when the mean is a fraction or decimal value and usually easier with a large number of scores.

In an experiment examining the effects Tai Chi on arthritis pain, Callahan select a large sample of individuals with doctor-diagnosed arthritis. Half of the participants immediately began a Tai Chi course and the other half waited 8 weeks before beginning. At the end of 8 weeks, the individuals who had experienced Tai Chi had less arthritis pain that those who had not participated in the course. a) Identify the independent variable for this study b) What scale of measurement is used for the independent variable? c) Identify the dependent variable for this study D) What scale of measurement is used for the dependent variable

a. The independent variable is taking the Tai Chi course versus not taking the course. b. Nominal scale because whether you take or do not take the course represents two different categories. c. The dependent variable is the amount of arthritis pain experienced. d. The amount of pain is measured with an interval or a ratio scale. In some cases, it is hard to tell the type between interval and ratio unless you have more information. For instance, can someone measure 0 on the pain scale. If so, it would be ratio. If not, it would be interval.

A population has a mean of mu=50 and a standard deviation of sigma=10 a) If 3 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 2, then what would be the new values for the mean and standard deviation

a. The mean is μ = 53 and the standard deviation is still σ = 10. b. The new mean is μ = 100 and the new standard deviation is σ = 20.

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? b) If you score were X=72, would you prefer s= 2 or s=10? Explain your answer

a. X = 84 has a much higher location in the distribution with s = 2. It is above the mean by three times the standard deviation. b. X = 72 is closer to average with s = 10. It is below the mean but less than one standard deviation below.

For the following set of scores: 8, 5, 9, 6, 8, 7, 4, 10, 6, 7 9, 7, 9, 9, 5, 8, 8, 6, 7, 10 a) Construct a frequency distribution table to organize the scores b) draw a frequency distribution histogram for these data

a. X f 10 2 9 4 8 4 7 . 4 6 3 5 . 2 4 . 1 b. Continous Graph, with .5 difference below and above

For the following set of scores, find the value of each expression: a) SUM X b) SUM X^2 c) SUM (X+3)

a. ΣX = 0 b. ΣX2 = 50 c. Σ(X + 3) = 15

What is the value of SS, the sum of the squared deviations, for the following population of N=4 scores? Scores: 1,4,6,1 a) 0 b) 18 c) 52 d) 144

b) 18

Each of the following is the sum of the scores for a population would the definitional formula be better choice than the computational formula for calculating SS. a) SUM X = 9 b) SUM X = 12 c) SUM X = 15 d) SUM X = 19

b) SUM X = 12

Standard deviation is probably the most commonly used value to describe the measure variability. Which of the following accurately describes the concept of standard deviation? a) the average distance between one score and another b) The average distance between a score and the mean c) the total distance from the smallest score to the largest score d) One half of the total distance from the smallest score to the largest score

b) The average distance between a score and the mean

For the following population of N=6 scores: 3, 1, 4, 3, 3, 4 a) Sketch a histogram showing the population distribution b) Locate the value of the population mean in your sketch, and make an estimate of the standard deviation c) Compute SS, variance, and standard deviation for the population.

b. The mean is μ = 18/6 = 3. The three scores of X = 3 are exactly equal to the mean (zero distance) and the greatest distance is 2 points for X = 1. The standard deviation appears to be about 1 point. c. SS = 6, σ2 = 1, σ = 1

What is the value of SS, the sum of the squared deviations, for the following sample? Scores: 1,4,0,1 a) 36 b) 18 c) 9 d) 3

c) 9

What is the variance for the following sample of n=4 scores? Scores; 2,5,1,2 a) 34/3= 11.33 b) 9/4= 2.25 c) 9/3= 3 d) squr root 3 = 173

c) 9/3= 3

What is the standard deviation for the following population of scores? Scores: 1, 3, 7, 4, 5 a) 20 b) 5 c) 4 d) 2

d) 2