Chapter 3-4

Question 1

1. If reaction time is X, then the value of Σ(X-M)^2 is

Answer 1

125068.9

Question 1

1. A study is conducted in which 12 participants press a button when they hear the first dirty word in a list of words. The time it takes them to press the button is recorded (their reaction times, in msec).
   The mean reaction time is

Answer 1

725.1

Question 2

1. The standard deviation of reaction time is

Answer 2

106.6

Question 3

1. The median reaction time is

Answer 3

750

Question 4

1. The 25th and 75th percentile points (without interpolation) are?

Select one:
a. 750 and 804
b. 603 and 823
c. 680 and 804
d.603 and 804

Answer 4

d.603 and 804

Question 5

1. The shape of the distribution is?

Select one:
a. asymptotic
b. symmetric
c. negatively skewed
d. positively skewed

Answer 5

c. negatively skewed

Question 6

Why compute sample variance?

Select one or more:
a. To find a number that best represents differences among subjects in a distribution
b. To find a number that best estimates σ2
c. To find a number that reduces sampling error
d. To find a number that best represents the typical subject in a distribution

Answer 6

a. To find a number that best represents differences among subjects in a distribution
b. To find a number that best estimates σ2

Question 7

Under what circumstances will the mean, the median, and the mode all have the same value?

Select one:
a. in a symmetrical, unimodal, asymptotic, distribution
b. this will always occur in a distribution with no sampling error
c. in a symmetrical, asymptotic distribution
d. in a skewed, bimodal distribution

Answer 7

a. in a symmetrical, unimodal, asymptotic, distribution

Question 8

In what sense is the mean the center of a distribution?

Select one:
a. M is like a balance point because Σ(X-M)=0 for every sample
b. M for the sample always equals μ for the population
c. M is the center because it is always the most probable score in the sample
d. M is the center because half the sample scores are always above it and half are below

Answer 8

a. M is like a balance point because Σ(X-M)=0 for every sample

Question 9

Why there is more than one method for measuring central tendency?

Select one or more:
a. because extreme outliers drastically affect the mode but not the mean or the median
b. because skewness makes the median better than the mean for indicating the center of the distribution
c. because the mode is the best measure of centrality when the distribution has more than one peak
d. because distributions differ in variance

Answer 9

b. because skewness makes the median better than the mean for indicating the center of the distribution
c. because the mode is the best measure of centrality when the distribution has more than one peak

Question 10

Which of the following is the best situation for using variance as a measure of a distribution’s variability?

Select one:
a. when the data are on an interval scale and the distribution is unimodal
b. in a distribution with large sampling error
c. in a symmetrical, unimodal distribution, with ordinal data
d. in a unimodal distribution with extreme outliers

Answer 10

a. when the data are on an interval scale and the distribution is unimodal

Question 11

Why is N the denominator of the formula for the sample mean while N-1 is the denominator for sample variance?

Select one:
a. because these denominators provide the most unbiassed estimates of μ and σ, respectively
b. because the mean is the center of X and the variance is average deviation from center
c. because the degrees of freedom for the mean is N and for variance it is N-1
d. because all X values are used for computing the mean but one of the values of X is not used in computing variance

Answer 11

a. because these denominators provide the most unbiassed estimates of μ and σ, respectively

Question 12

Why is Σ(X-M)2 used as the numerator of the formula for sample variance instead of Σ(X-M)?

Select one or more:
a. because Σ(X-M)^2 < Σ(X-any other value)^2
b. because s^2= Σ(X-M)^2/(N)
c. because Σ(X-M)^2 is always equal 0 by definition
d. because Σ(X-M)=0 for all samples, so variance would be 0 for all samples

Answer 12

a. because Σ(X-M)^2 < Σ(X-any other value)^2
d. because Σ(X-M)=0 for all samples, so variance would be 0 for all samples

Question 13

What is the difference between μ and M?

Select one:
a. μ is the variance and M is the mean
b. μ is the median and M is the mean
c. μ is the mean of the sample and M is the mean of the population
d. μ is the mean of the population and M is the mean of the sample

Answer 13

d. μ is the mean of the population and M is the mean of the sample

Question 14

The general purpose of computing central tendency is to

Select one or more:
a. find a number that best represents those on the outskirts of the distribution
b. estimate the center of a given population or data set
c. find a single number that is most representative of the overall sample, taking into account all data points
d. find a number that reduces sampling error

Answer 14

b. estimate the center of a given population or data set
c. find a single number that is most representative of the overall sample, taking into account all data points

Question 15

5. The following are summary graphs and statistics for the number of IPT questions answered correctly (0 to 9 possible), with the subjects grouped by whether or not they ever owned a dog, in an experiment like the one we conducted by a previous set of students.

What percent of subjects in the Non Dog Owner group got scores (# of correct answers) that were also observed in the Dog Owner Group?

Answer 15

56

Question 16

5. What percent of subjects in the Dog Owner group got scores that were also observed in the Non Dog Owner Group?

Answer 16

100

Question 17

5. What percent of subjects in the Non Dog Owner group got fewer correct responses than any subject in the Dog Owner Group?

Answer 17

2

Question 18

5. What percent of subjects in the Non Dog Owner group got more correct responses than any subject in the Dog Owner Group?

Answer 18

42

Question 19

5. Which group has more inter-subject differences, and how did you determine this?

Select one:
a. The Non Dog Owner group, because its standard deviation is larger
b. The Non Dog Owner group, because it has the highest score
c. The Dog Owner group, because it is a smaller sample
d. The Dog Owner group, because its sampling error is larger

Answer 19

a. The Non Dog Owner group, because its standard deviation is larger

Question 20

5. What do the means alone tell you?

Select one or more:
a. μNonOwner > μOwner
b. The average non-dog owner answered more questions correctly
c. The average dog owner answered fewer questions correctly
d. The two groups do not differ

Answer 20

b. The average non-dog owner answered more questions correctly
c. The average dog owner answered fewer questions correctly

Question 21

5. What does the bar graph on its own (the right most graph) tell you?

Select one or more:
a. We can reject the null hypothesis that μNonOwner = MNonOwner
b. The difference between groups is smaller than the variation within the Non-Dog Owner group
c. The Non Dog Owner group subjects differ more from each other than the Dog Owners do
d. We can accept the alternative hypothesis that μNonOwner > μOwner

Answer 21

b. The difference between groups is smaller than the variation within the Non-Dog Owner group
c. The Non Dog Owner group subjects differ more from each other than the Dog Owners do

Question 22

5. What do the histograms tell you that neither the means alone nor the bar graphs alone tell you?

Select one or more:
a. We can accept the alternative hypothesis that μNonOwner > μOwner
b. It is misleading to evaluate the meaning of a single number without considering the context
c. The Dog Owner performance totally overlaps with the Non Dog Owners
d. We can reject the null hypothesis that μNonOwner = MNonOwner

Answer 22

b. It is misleading to evaluate the meaning of a single number without considering the context
c. The Dog Owner performance totally overlaps with the Non Dog Owners

Question 23

2. The following is a grouped distribution of scores on an exam graded in increments of 1 point:
   If ΣX= 2456, then the mean is

Answer 23

54.6

Question 24

2. The missing frequency of the interval 70-74 is

Answer 24

9

Question 25

2. The fact that you could calculate the missing frequency of the interval 70-74 means

Select one:
a. the mean and median were in the same interval
b. ΣX= 2456
c. MX = μX
d. degrees of freedom (df)= N-1

Answer 25

d. degrees of freedom (df)= N-1

Question 26

2. The standard deviation

Select one:
a. is 21.2
b. can’t be determined from the information given
c. is larger than the interquartile range
d. is the square root of 21.2

Answer 26

b. can’t be determined from the information given

Question 27

2. The grouped frequency distribution tells you

Select one or more:
a. the distribution is highly skewed
b. the distribution has one mode
c. the distribution is fairly symmetrical
d. the distribution is asymptotic

Answer 27

b. the distribution has one mode
c. the distribution is fairly symmetrical
d. the distribution is asymptotic