Statistics (1st midterm) Lessons 1.5/1.6/2.2/2.3/3.2/3.3

In a stem-and-leaf plot, what numbers are the stem and what numbers are the leaf in number 273?

27 is the stem and 3 is the leaf

An experiment in which each experimental unit is randomly assigned to a treatment group is said to have a ______ ______ design.

completely randomized

A measure of ______ is a measure of how spread out the data are or how much the data vary within the distribution.

dispersion

While you use empirical or Chebyshev's when dealing with a bell shape?

empirical

The height of each rectangle is the ____ or ____ _____ of the class.

frequency; relative frequency

A ____ is constructed using rectangles for each class of data.

histogram

The ______ the standard deviation, the _____ dispersion the distribution has.

larger; more

The ______ class limit is the smallest value within the class and the ______ class limit is the largest value within the class.

lower; upper

The standard deviation is used in conjunction with the _____ to numerically describe distributions that are bell shaped. A. range B. mode C. variance D. mean E. median

mean

The _____ measures the center of the distribution, which the standard deviation measures the _____ of the distribution. A. mean B. variance C. standard deviation D. range A. range B. center C. spread

mean; spread

The errors that result from the aforementioned bias are called ______ ______.

non sampling errors

In the _____ ______ design the experimental units are separated into homogeneous groups called blocks. Then for each block, the experimental units are randomly assigned to the levels of treatment.

randomized block design

The _____, of a variable is the difference between the largest and smallest data values.

range

ANY TIME one uses a sample to estimate information about a population, there will be a ______ ______. This occurs simply because a sample gives incomplete information about a population.

sampling error.

A distribution is ______ ______ if the tail to the left of the peak is longer than the tail to the right of the peak.

skewed left

A distribution is _____ _____ if the tail to the right of the peak is longer than the tail to the left of the peak.

skewed right

The _____ ______ of a variable measures how far, on average, the data values are from the mean of that data set.

standard deviation

A ______-____-_____ plot is a quantitative display of every data value in a data set.

stem-and-leaf

If the frequency of each value of a variable is (roughly) evenly distributed among values of the variable, we say the variable has a ______ distribution.

uniform

Define placebo. Choose the correct answer below. A. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication. B. Grouping together similar experimental units. C. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable. D. Using treatments on many experimental units.

A. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication.

To help assess student learning in her geography courses, a geography professor at a university implemented pre-and post-tests for her geography students. A knowledge-gained score was obtained by taking the difference of the two test scores. What type of experimental design is this? A. Matched pair B. Case-control C. Completely randomized design D. Randomized block design What is the treatment? A. Background of student B. Type of school C. Geography scores D. Geography course

A. Matched pair D. Geography course

For a number of people living in a household, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed right. A. Skewed left B. Skewed right C. Uniform D. Bell shaped

A. Skewed right

What is an advantage of using a stem-and-leaf plot instead of a histogram? A. Stem-and-leaf plots contain original data values where histograms do not. B. Stem-and-leaf plots easily organize data of all sizes where histograms to not. C. Stem-and-leaf plots graph qualitative data where histograms do not. D. Stem-and-leaf plots show data clusters where histograms do not.

A. Stem-and-leaf plots contain original data values where histograms do not.

What makes the range less desirable than the standard deviation as a measure of dispersion? A. The range does not use all the observations. B. The range is biased. C. The range is resistant to extreme values. D. The range describes how far, on average, each observation is from the mean.

A. The range does not use all the observations.

What is a disadvantage of using a stem-and-leaf plot instead of a histogram? A. Histograms show data clusters where stem-and-leaf plots do not. B. Histograms easily organize data of all sizes where stem-and-leaf plots do not. C. Histograms contain original data values where stem-and-leaf plots do not. D. Histograms graph quantitative data where stem-and-leaf plots do not.

B. Histograms easily organize data of all sizes where stem-and-leaf plots do not.

What is replication in an experiment? A. Replication is grouping together similar experimental units and then using random assignment. B. Replication is applying each treatment to more than one experimental unit. C. Replication is randomly assigning each experimental unit to a treatment. D. Replication is pairing up related experimental units.

B. Replication is applying each treatment to more than one experimental unit.

Define experimental unit. Choose the correct answer below. A. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication. B. Any combination of the values of the factors (explanatory variables). C. A person, object, or some other well-defined item upon which a treatment is applied. D. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable.

C. A person, object, or some other well-defined item which a treatment is applied.

Define factor. Choose the correct answer below. A. Grouping together similar experimental units. B. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication. C. A variable whose effect on the response variable is to be assessed by the experimenter. D. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable.

C. A variable whose effect on the response variable is to be assessed by the experimenter.

In a statistics class, the standard deviation of the heights of all students was 4.1 inches. The standard deviation of the heights of males was 3.3 inches and the standard deviation of females was 3.2 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately? A. The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the smaller the sample, the smaller the sample standard deviation. B. The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because there is more dispersion in the male and female samples than the entire class. C. The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the distribution of the entire class has more dispersion. D. The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the male and female sample sizes are smaller than the sample of the entire class.

C. The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the distribution of the entire class has more dispersion.

What is the fifth step in conducting an experiment?

Conduct the experiment. Ex: randomly assign units to treatments, apply treatments, record and summarize the data

Define treatment. Choose the correct answer below. A. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable. B. The number of individuals in the experiment. C. A controlled study to determine the effect varying one or more explanatory variables or factors has on a response variable. D. Any combination of the values of the factors (explanatory variables).

D. Any combination of the values of the factors (explanatory variables).

Define response variable. Choose the correct answer below. A. The variable whose effect on the response variable is to be assessed by the experimenter. B. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication. C. The effect of two factors (explanatory variables on the response variable) cannot be distinguished. D. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable.

D. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable.

True or False: Chebyshev's inequality applies to all distributions regardless of shape, but the empirical rule holds only for distributions that are bell shaped. A. False, both Chebyshev's inequality and the emperical rule will only work for bell-shaped distributions. B. False, the empirical rule is less precise than Chebyshev's inequality, but will work for any distribution, while Bhebyshev's inequality only works for bell-shaped distributions. C. False, both Chebyshev's inequality and the empirical rule will work for any distribution. D. True, Chebyshev's inequality is less precise than the empirical rule, but will work for any distribution, while the empirical rule only works for bell-shaped distributions.

D. True, Chebyshev's inequality is less precise than the empirical rule, but will work for any distribution, while the empirical rule only works for bell-shaped distributions.

True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure. A. False, because the standard deviation of measures the spread of the distribution, not the dispersion of the distribution. B. False, because the larger the standard deviation is, the less dispersion the distribution has. C. True, because the standard deviation is the difference between the largest and smallest observation. When the standard deviation is larger, there is more distance between the largest and smallest observation, and therefore, more dispersion in the distribution. D. True, because the standard deviation describes how far on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore dispersed.

D. True, because the standard deviation in the distribution describes how far on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore dispersed.

What is the second step in conducting an experiment?

Determine all factors affecting the response variable. Ex: identify factors that are controlled or uncontrolled

What is the third step in conducting an experiment?

Determine the number and level of all factors? Ex: set one level of a factor

What is the fourth step in conducting an experiment?

Determine the number of experimental units. Ex: might determine how much money you have

What is the first step in conducting an experiment?

Identify the research objective/problem to be solved. Ex: be specific, identify population, identify response variable

________ bias occurs when the selected individuals who do not respond to the survey have different opinions from those who do.

Nonresponse

______ bias exists when the true feelings of respondents are not reflected in their answers to the survey.

Response

_____ bias occurs when the technique used to obtain the sample tends to favor one part of the population over another.

Sampling

What are three commons sources of bias?

Sampling Bias Nonresponse Bias Response Bias

What is the last step in conducting an experiment?

Test the claim. Ex: compare results across treatments, take average test scores, etc...

In a _____-______ distribution the highest frequency occurs in the middle. Frequencies "tail off" to the left and right of the middle in a symmetrical way.

bell-shaped

A sample has _____ is the data do not adequately represent the population.

bias

If the data are discrete and there are only a few different values of the variable, then each value will be considered as a ______ (or category).

class

The _____ _____ is the difference between consecutive lower class limits.

class width

If the data are discrete, but there are many different values of the variable, or if the data are continuous, then ________ __ _____ will be created using intervals of numbers.

classes of data