Statistics Chapter 1

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

individual

True or False In​ statistics, results are always reported with​ 100% certainty. Choose the correct answer below.

False. In​ statistics, results are not reported with​ 100% certainty. Because statistical studies draw on​ samples, and because there is variation within​ groups, results cannot be reported with​ 100% certainty.

True or False Statistical studies are not concerned with understanding the sources of variability in​ data, only with describing the variability in the data. Choose the correct answer below.

False. Statistical studies are concerned with both describing the variability in the data and understanding the sources of variability in data. Understanding the sources allows researchers to control it and reach better conclusions.

Determine the level of measurement of the variable. Rankings of musicians

Ordinal

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

Parameter

Determine whether the underlined value is a parameter or a statistic. The average score for a class of 28 students taking a calculus midterm exam was 72 %

The value is a parameter because the class of 28 students is a population.

Determine whether the quantitative variable is discrete or continuous. Number of points scored in a baseball game

The variable is discrete because it is countable.

Determine whether the variable is qualitative or quantitative. Eye color

The variable is qualitative because it is an attribute characteristic

Determine whether the variable is qualitative or quantitative. Favorite city

The variable is qualitative because it is an attribute characteristic.

True or False Suppose three different individuals conduct the same statistical​ study, such as estimating the average commute time of students at a college. It is possible that all three studies end up with different results. Choose the correct answer below.

True. Statistical studies typically look at samples rather than entire populations. Since each study is likely to draw different​ samples, it is quite possible that each study ends up with different​ results, due to variability in the data.

​_________ are the characteristics of the individuals of the population being studied

Variables

The data on the right relate to characteristics of​ high-definition televisions A through E. 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? - The​ high-definition television setups A through E. What are the variables and their corresponding data being​ studied? - Size ​(43​, 58​, 49​, 44​, 57​), screen type ​(Plasma​, Projection​, Projection​, Projection, Projection, Plasma​), and number of channels available number of channels available ​(298​, 110​, 422​, 269​, 289​) Determine whether each variable is​ qualitative, continuous, or discrete. - Size is a continuous variable. - Screen type is a qualitative variable. - Number of channels available is a discrete variable.

A news service conducted a survey of 1098 adults ages 18 years or older in a certain​ country, August 31−September ​2, 2015. 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 1098 individuals​ surveyed, 34​% indicated that 51 cents or more is wasted. The news service reported that 34​% 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 6​% and a 95​% level of confidence. Complete parts ​(a) through​ (e) below. ​(a) What is the research​ objective? ​(b) What is the​ population? (c ) What is the​ sample? (d) List the descriptive statistics. Choose the correct answer below. (e)What can be inferred from this​ survey?

(a) To determine the percent of adults in the country who believe the federal government wastes 51 cents or more of every dollar (b) Adults in the country aged 18 years or older (c ) The 1098 adults in the country that were surveyed (d) 34​% of the individuals surveyed indicated that 51 cents or more is wasted. (e) The news service is 95​% confident 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 28​% and 40​%.

​A(n) ___________ is a numerical summary of a sample. ​

Statistic

Define 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.

Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. In a phone survey of 100 random homes in a country, 21 % of families had garages.

Statistic​, because the data set of 100 random homes is a sample.