STATS

A salesperson obtained a systematic sample size of 25 from a list of 500 clients. To do so, he randomly selected a number from 1 to 20, obtaining the number 13. He included in the sample the 13th client on the list and every 20th client thereafter. List the numbers that correspond to the 25 clients selected.

13,33,...,493 Population Size ------------------ = round down to equal k Sample Size Randomly selected number between 1 and k = p p, p + k, p + 2k, p + (n - 1)k

% Data within 1 standard deviation

68%

% Data within 2 standard deviations

95%

% Data within 3 standard deviations

99.7%

What is an observational study? What is a designed experiment? Which allows the researcher to claim causation between an explanatory variable and a response variable? What is an observational study? What is a designed experiment? Which allows the researcher to claim causation between an explanatory variable and a response variable?

An observational study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. A designed experiment is when a researcher assigns individuals to a certain group, intentionally changing the value of an explanatory variable, and then recording the value of the response variable for each group. A designed experiment

A quality-control manager randomly selects 20 bottles of tomato sauce that were filled on March 28 to assess the calibration of the filling machine. What is the population in the study? What is the sample in the study?

Bottles of tomato sauce produced in the plant on March 28. The 20 bottles of tomato sauce produced in the plant on March 28.

To determine the customer opinion of their pricing, Home Depot randomly selects 90 check out lines during a certain week and surveys all customers in the check out lines. What type of sampling is used?

Cluster

A(n) ____ is obtained by dividing the population into groups and selecting all individuals from within a random sample of groups.

Cluster Sample

What is meant by confounding? What is a lurking variable?

Confounding in a study occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study. A lurking variable is an explanatory variable that was not considered in a study, but is also affected by the casual relationship of the explanatory variables in the study. In addition, lurking variables are typically related to explanatory variables in the study.

A television station asks its viewers to call in their opinion regarding the variety of sports programming. What type of sampling is used?

Convenience

____ statistics consist of organizing and summarizing information collected, while ____ statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.

Descriptive Inferential

A student entering a doctoral program in educational psychology is required to select three courses from the list of courses provided as part of his or her program. List all possible three-course selections. Comment on the likelihood that EPR 651, EPR 602, and EPR 631 will be selected.

Ensure no repeating answers in selection There is a 1 in 10 likelihood.

What does it mean if a statistic is resistant?

Extreme values (very large or small) relative to the data do not affect its value substantially.

A published study looked at levels of a protein released when the heart is stressed. Researchers measured the protein levels in 1031 patients and followed their health for seven years. People with the highest protein level were 1 1/2 times more likely to die from any cause than those with the lowest. The lead researcher said, "It sort of tells you that no matter what conditions you have, higher levels of these proteins are associated with worse outcomes." Identify the research question the study addresses Identify the population. Identify the sample. Identify the descriptive statistics. Identify the inferences of the study.

How is the level of a certain protein associated with a person's health? All people. The 1031 patients in the study. People with the highest levels of the protein were 1.5 times more likely to die than those with the lowest values. Higher levels of the protein are associated with worse outcomes.

A(n) ____ is a person or object that is a member of the population being studied.

Individual

Determine the level of measurement of the variable. Years of elections: 1988, 1992, 1996, 2000, and 2004

Interval

Determine the level of measurement of the variable. Dress color

Nominal

Determine the level of measurement of the variable. Nation of origin

Nominal

It is extremely important for a researcher to clearly define the variables in a study because this helps to determine the type of analysis that can be performed on the data. For example, if a researcher wanted to describe cities based on zip code, what level of measurement would the variable "zip code" be? Now suppose the researcher felt that certain cities with a higher population density received higher zip codes. Does the level of measurement of the variable change? If so, how? What is the level of measurement of the variable "zip code" in the original scenario? Does the level of measurement of the variable change in the second scenario?

Nominal Yes, it changes to ordinal

Distinguish between nonsampling error and sampling error.

Nonsampling error is the error that results from the process of obtaining the data. Sampling error is the error that results because a sample is being used to estimate information about a population.

What does it mean when sampling is done without replacement?

Once an individual is selected, the individual cannot be selected again.

Determine the level of measurement of the variable. Positions of persons in a line

Ordinal

Determine the level of measurement of the variable. Finishing ranks of swimmers in a swim meet

Ordinal

Determine where the given value is a statistic or parameter. In a study of all 2771 seniors at a college, it is found that 25% own a vehicle.

Parameter because the value is a numerical measurement describing a characteristic of a population.

Determine whether the underlined numerical value is a parameter or a statistic. *Two* students in a class of 29 have red hair.

Parameter, because the data set of all 29 students is a population.

Determine the level of measurement of the variable. Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years

Ratio

For wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 90 customers and asks them about their level of satisfaction with the company. What type of sampling is used?

Simple random

Choose the correct definition of Statistics

Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw a conclusion and answer questions. In addition, statistics is about providing a measure of confidence in any conclusions.

To determine her body temperature, Denise divides up her day into three parts: morning, afternoon, and evening. She then measures her body temperature at 3 randomly selected times during each part of the day. What type of sampling is used?

Stratified

Sample standard deviation on TI 83+ is

Sx

Sample variance on TI 83+ is

Sx squared

To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at Ford selects every 15th truck that comes off the assembly line starting with the tenth until she obtains a sample of 60 trucks. What type of sampling is used?

Systematic

The Gallup Organization contacts 1183 teenagers who are 13 to 17 years of age and live in the United States and asks whether or not they had attended a concert this past year. What is the population in the study? What is the sample in the study?

Teenagers who are 13 to 17 years of age and live in the United States. The 1183 teenagers who are 13 to 17 years of age and live in the United States.

The data on the right relate to setups A through E of widescreen high-definition televisions. Setup | Size (in) | Screen Type | Number of Channels Available A | 60 | Plasma | 298 B | 42 | Projection | 105 C | 40 | Projection | 422 D | 58 | Projection | 270 E | 45 | Projection | 289 Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete. What are the individuals being studied? What are the variables and their corresponding data being studied? Size is a ____ variable. Screen type is a ____ variable. Number of channels available is a ____ variable.

The setups A through E of widescreen high-definition televisions. Size (60, 42, 40, 58, 45), screen type (Plasma, Projection, Projection, Projection, Projection), and number of channels available (298, 105, 422, 270, 289) Continuous Qualitative Discrete

Determine whether the study depicts an observational study or an experiment. Fifty patients on aspirin are divided into two groups. One group is treated with a new anti-ulcer drug. The other is not. After one month, both groups are questioned about their stomach pain.

The study is an experiment because the researchers control one variable to determine the effect on the response variable.

Does the description correspond to an observational study or an experiment. Fifty patients with lung cancer are divided into two groups. One group receives an experimental drug to fight cancer, the other a placebo. After two years, the spread of the cancer is measured. Does the description correspond to an observational study or an experiment?

The study is an experiment because the researchers control one variable to determine the effect on the response variable.

Determine whether the study depicts an observational study or an experiment. A poll is conducted by a school's math department in which fourth-grade students are asked if they prefer to be in their math class or their English class.

The study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable.

Determine whether the study depicts an observational study or an experiment. A survey is conducted asking 250 people, "Do you prefer soup A or soup B?"

The study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable.

Determine whether the underlined value is a parameter or a statistic. In a survey of 1,011 people age 50 or older, *73%* agreed with the statement "I believe in life after death."

The value is a statistic because the 1,011 people age 50 or older are a sample.

Determine whether the quantitative variable is discrete or continuous. Number of lightning strikes in a city in one year.

The variable is discrete because it is countable.

Determine whether the quantitative variable is discrete or continuous. Number of pieces of lumber used to make a deck.

The variable is discrete because it is countable.

Determine whether the quantitative variable is discrete or continuous. Passes made by a defenseman in a hockey game.

The variable is discrete because it is countable.

Determine whether the variable is qualitative or quantitative. Address

The variable is qualitative because it is an attribute classification.

Determine whether the variable is qualitative or quantitative. Street name of address.

The variable is qualitative because it is an attribute classification.

Determine whether the variable is qualitative or quantitative. Amount of disk space in gigabytes.

The variable is quantitative because it is a numerical measure.

A study conducted by researchers was designed "to determine if application of duct tape is as effective as cryotherapy in the treatment of common warts." The researchers randomly divided 50 patients into two groups. The 25 patients in group 1 had their warts treated by applying duct tape. The 25 patients in group 2 had their warts treated by cryotherapy. Once the treatments were complete, it was determined that 56% of the patients in group 1 and 66% of the patients in group 2 had complete resolution of their warts. The researchers concluded that cryotherapy is significantly more effective in treating warts than duct tape. Identify the research objective. Identify the sample. List the descriptive statistics. State the conclusion of the study.

To determine if duct tape is as effective as cryotherapy in treating warts. The 50 patients with warts. 56% of patients in group 1 and 66% of patients in group 2 with complete resolution. Cryotherapy is significantly more effective than duct tape in treating warts.

A news service conducted a survey of 1021 adults age 18 years or older in a certain country, August 31 - September 2, 2009. The respondents were asked, "Of every tax dollar that goes to the federal government, how many cents of each dollar would you say are wasted?" Of the 1021 individuals surveyed, 35% indicated that 51 cents or more is wasted. The new service reported that 35% of all adults in the country 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of 5% and a 90% level of confidence. What is the research objective? What is the population? What is the sample? List the descriptive statistics. What can be inferred from this survey?

To determine the proportion of adults in the country who believe the federal government wastes 51 cents or more of every dollar. Adults in the country aged 18 years or older. The 1021 adults in the country that were surveyed. Of the 1021 individuals surveyed, 35% indicated that 51 cents or more is wasted. The news service is 90% certain that the percentage of all adults in the country who believe the federal government wastes 51 cents or more of every dollar received is between 30% and 40%.

Inferences based on voluntary response samples are generally not reliable. True or false

True, because I is often the case that the individuals who volunteer do not accurately represent the group.

____ are the characteristics of the individuals of the population being studied.

Variables

More convincing data has a ____ z-score

lower

The standard deviation is used in conjunction with the ____ to numerically describe distributions that are bell shaped The ____ measures the center of the distribution, while the standard deviation measures the ____ of the distribution.

mean; mean; spread

Which measure of central tendency best describes the weight of the candy?

median because the data is skewed mean is useful when the data is symmetrical

Population standard deviation on TI 83+ is

ox

Population variance on TI 83+ is

ox squared

A(n) ____ is a numerical summary of a population.

parameter

The distribution of violent crime is ____

skewed right

A(n) ____ is a numerical summary of a sample.

statistic

_x < M when

the histogram is skewed left

_x > M when

the histogram is skewed right

_x = M when

the histogram is symmetrical