Chapter 1
1. A researcher is investigating the effectiveness of a treatment for adolescent boys who are taking medication for depression. A group of 30 boys is selected and half receive the new treatment in addition to their medication and the other half continue to take their medication without treatment. For this study,
a. Identify the population.
b. Identify the sample
a) The population is the entire set of adolescent boys who take medication for depression
b) The sample is the group of 30 boys selected for this study
1) With which scale of measure do we use a histogram?
2) With which scale of measure do we use a frequency polygon?
3) With which scales of measure do we use a bar graph?
1) Interval or Ratio Scales
2) Interval or Ratio Scales
3) Nominal or Ordinal Scales
Identify if the statement below is true or false!
“It is possible to have more than one mode in a distribution”
(TRUE)
Identify if this statement is true or false!
“Samples tend to be more variable than the populations from which the are drawn”
False
4. 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. μ= 45 and σ= 10
b. μ= 45 and σ= 2
c. μ= 90 and σ= 20
d. μ= 60 and σ= 20
a) 50-45 / 10 = 0.50
0.50 - central
b) 50-45 / 2 = 2.50
2.50 - extreme
c) 50-90 / 20 = -2.00
-2.00 - extreme
d) 50 - 60 / 20 = -0.50
-0.50 - central
2. Define the terms parameter and statistic. Be sure that the concept of the population and sample are included in your definitions.
A parameter is a characteristic (usually numerical) that describes a population.
A statistic is a characteristic (usually numerical) that describes a sample
Identify each of these distributions:
Screen Share (Different Distribution Document)
1) Negatively Skewed Distribution
2) Normal Distribution
3) Positively Skewed Distribution
4) Bimodal Distribution
6. One sample has a mean of M = 4 and a second sample has a mean of M= 8.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= 7scores?
b. What is the mean for the combined set if the first sample has n= 3 and the second sample has n= 7?
a) M1= 4 and n1=7 -- ΣX1 = M1xN1= 4x7= 28
M2=8 and n2 =7 -- ΣX2 = M2xN2= 8x7= 56
Combined Mean = ΣX1 + ΣX2 / n1+n2 =
28+56 / 7+7 = 84 / 14 = 6
b) M1= 4 and n1=3 -- ΣX1 = M1xN1= 4x3= 12
M2=8 and n2 =7 -- ΣX2 = M2xN2= 8x7= 56
Combined Mean = ΣX1 + ΣX2 / n1+n2 =
12+56 / 3+7 = 68 / 10 = 6.8
4. 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.)
SS= 32
σ2= 4
σ= 2
(See Chapter 4 Problems)
5. A distribution of exam scores has a mean of μ= 80.
a. If your score is X= 86, which standard deviation would give you a better grade: σ=4 or σ=8?
b. If your score is X= 74, which standard deviation would give you a better grade: σ=4 or σ=8?
a) x = 86 and μ = 80
For σ= 4
z = 86-80 / 4 = 1.50 This is the better score
For σ= 8
z = 86-80 / 8 = 0.75
b) x = 74 and μ = 80
For σ= 4
z = 74-80 / 4 = -1.50
For σ= 8
z = 74-80 / 8 = -0.75 This is the better score
7. A researcher would like to evaluate the claim that large doses of vitamin C can help prevent the common cold. One group of participants is given a large dose of the vitamin (500 mgper day), and a second group is given a placebo (sugar pill). The researcher records the number of colds each individual experiences during the 3-month winter season.
a. Identify the independent variable for this study.
b. Identify the dependent variable for this study.
c. Is the dependent variable discrete or continuous?
d. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable?
a) Independent variable is dosage of Vitamin C (500 mg. vs. placebo)
b) Dependent variable is number of colds
c) Discrete (either have a cold or you don’t, no in-between)
d) Ratio (zero means no cold)
Find each value requested for the distribution of scores in the following table.
n = ?
∑X = ?
∑X² = ?
X f
5 2
4 3
3 1
2 4
1 2
n = ∑f = 2 + 3 + 1 + 4 + 2 = 12
∑fX = (2 x 5) + (3 x 4) + (1 x 3) + (4 x 2) + (2 x 1) = 35
∑X² = (2 x 5²) + (3 x 4²) + (1 x 3²) + (4 x 2²) + (2 x 1²) = 125
Find the mean, median, and mode for the scores in the following frequency distribution table:
X f
10 1
9 2
8 3
7 3
6 4
5 2
Mean = 7.13
Median = 7
Mode = 6
(Refer to Chapter 3 Problems)
6. 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.)
SS = 36
s2= 9
s= 3
(See Chapter 4 Problems)
6. A distribution with a mean of μ= 56 and a standard deviation of σ= 20 is transformed into a standardized distribution with μ= 50 and σ= 10.
Find the new, standardized score for each of the following values from the original population.
a. X = 46
b. X = 76
a) z = 46 - 56 / 20 = -.50
Xnew = 50+(-.50)(10) = 45
b) z = 76 - 56 / 20 = 1.00
Xnew = 50 + (1.00)(10) = 60
For each of the following, determine whether the variable being measured is discrete or continuous and explain your answer.
a. Social networking (time spent on Facebook)
b. Family size (number of siblings)
c. Preference between digital or analog watch
d. Number of correct answers on a multiple-choice statistic quiz
a) Continuous. Amount of time is infinitely divisible.
b) Discrete. Number of siblings is whole number that can’t be divided.
c) Discrete. Analog and digital are two separate and distinct categories.
d) Discrete.*Assuming the underlying variable is literally “the number of correct answers, ”discrete would be appropriate since we’re dealing with separate, indivisible units.
Identify these the scales of measure and which frequency distribution graph would be appropriate. (*Hint: Think NOIR and histogram/frequency polygon and bar graphs)
a) Age measured in years
b) Age measured with the categories young, middle-age, and older
a) would be histogram/frequency polygon since the scale of measure is ratio
b) would be a bar graph since the scale of measure is ordinal