Chpt 1 - Introduction

Question 1

Statistics ___________ numerical or non-numerical data

Answer 1

Collect

Question 2

Statistics __________ data for the purpose of making generalizations and decisions

Answer 2

Analyze

Question 3

What is the core of statistics?

Answer 3

Data

Question 4

What is data?

Answer 4

Any information that has been collected

Question 5

Is data always numerical?

Answer 5

No

For example, which political party does someone support is not numerical

Another example is a yes/no answer to a question

Question 6

What is statistics?

Answer 6

The science of organizing and summarizing data, either numerical or non-numerical, to provide useful and accessible information about a particular subject

Question 7

What are the 4 steps to statistics?

Answer 7

1. collect data
2. summarize data
3. analyze and interpret data
4. draw conclusion from data

Question 8

What are the 2 different ways to classify statistical sudies?

Answer 8

Method 1 - descriptive statistics or inferential statistics

Method 2 - observational studies or designed experiments

Question 9

What is the purpose of the descriptive statistics study?

Answer 9

Summarize data

Examine and explore information for INTRINSIC interest only

For example, if we wanted to know about 100 students but only had enough time to ask 5 students, if we only talk about the 5 students we asked, that’s descriptive statistics

Basically, we are only describing the data we already have

Question 10

What is the purpose of the inferential statistics study?

Answer 10

To use information from a sample to draw a conclusion about the population

For example, if we wanted to know about 100 students but only had enough time to ask 5 students, and we use this sample information to make a conclusion about the whole 100 students

Basically, we are making inferences of a population based on the information we have

Question 11

What does inferential statistics consist of?

Answer 11

Methods of drawing and measuring the reliability of conclusions about a population based on information obtained from a sample of the population

Question 12

What does descriptive statistics consist of?

Answer 12

Methods for organizing and summarizing information and may include:

• Constructing graphs and tables
• Calculating various numerical measures such as averages, variations, and percentiles

Question 13

What is a population?

Answer 13

A collection of ALL individuals of items under consideration in a statistical study

Question 14

What is a sample?

Answer 14

Part of a population from which information is obtained

Question 15

What is the notation for the population size?

Answer 15

N

(Make sure it’s a capital letter)

Question 16

What is the notation for the sample size?

Answer 16

n

(make sure it’s lower case)

Question 17

What is the number of individuals in a population called?

Answer 17

Population size

Question 18

What is the number of individual in a sample called?

Answer 18

Sample size

Question 19

How are descriptive statistics and inferential statics interrelated?

Answer 19

Before carrying out an inferential analysis, descriptive statistics should be applied to organize and summarize information from a sample. This step helps us to choose appropriate inferential methods.

Question 20

In a STAT151 class of 60 students, the average score of 20 randomly selected
students is 71/100. Among these 20 students, 5 of them got scores among 80-100; 12 of them got scores among 50-79; and 3 of them are lower than 49. Is this study descriptive or inferential?

Answer 20

Discriptive

Question 21

In a national poll, 1000 adults were asked the following question: “If you won 10
million dollars in a lottery, would you continue to work, or would you stop working?” Based on the results of this poll, researchers made a conclusion “At least 60% Canadians would still work even if they won millions.” Is this study descriptive or inferential?

Answer 21

Inferential

Question 22

What is an observational study?

Answer 22

Researches simply observe characteristics and take measurements. The data are collected without any plan

Question 23

What is a designed experiement?

Answer 23

Researches first impose treatments and controls, and then observe characteristics and take measurements. The data are collected with a “plan”

Question 24

When the instructor asks 5 students about if they know what statistics are before the class even starts, what type of study is this? What type of study would it be if this question was asked at the end of the stats class?

Answer 24

Observational

Designed experiment (we have changed something to change the effect)

Question 25

One hundred 30-year-old people participated a project studying the relationship between exercise and a person’s fitness. These participants were randomly assigned into two groups. In Group 1, 50 participants were asked to do exercise more than 5 hours per week. The 50 participants in Group 2 were asked to do exercise less than 2 hours per week. Their body mass index (BMI) were measured after 6 months, analyzed, and interpreted. Is this an observational study or a designed experiment? Suppose that participants in group 1 significantly decreased BMI than group 2. Can we conclude that a person will become fit from doing a lot of exercise?

Answer 25

Designed experiment Yes, because it's a designed experiment that can help us determine causation

Question 26

A scientist was interested to know if smoking is a risk factor for lung cancer. She randomly selected 500 people and summarized the data obtained: smoker w/ lung CA: 200 smoker w/o lung CA: 60 nonsmoker w/ lung CA: 100 nonsmoker w/o lung CA: 140 Totals: smokers - 260 nonsmokers - 240 w/ lung CA: 300 w/o lung CA: 200 Is this an observational study or a designed experiment? Can we conclude that smoking is a risk factor for lung CA?

Answer 26

Observational study While we know as common knowledge that smoking can cause cancer, this is not a designed experiment, just an observational study, so causation cannot be determined

Question 27

What are the two main methods for collecting data used in STATS 151?

Answer 27

Census Sample

Question 28

What is census data collection? Why would this be a less attractive option to use?

Answer 28

Collect data from all individuals in the population It is time consuming and expensive

Question 29

What is sampling data collection?

Answer 29

Collecting data from a sample of the population We need to make sure the sample is representative of the population

Question 30

How often is the census collected in Canada?

Answer 30

Every 5 years

Question 31

What is the main type of sampling done in STATs 151?

Answer 31

Simple random sampling

Question 32

What is simple random sampling?

Answer 32

A sample taken in a way that each sample with the sample size has equal chance of being selected It depends on how they were selected, not the sample itself

Question 33

If a population has 5 letter, A, B, C, D, and E, what are the possible samples with the sample size n=2

Answer 33

A, B A, C A, D A, E B, C B, D B, E C, D C, E D, E

Question 34

Consider a population containing 3 students, Anna, Bruce, and Cindy (ABC lol). All possible samples have a sample size n=2, what are all the options? If all of these samples have an equal chance to be selected, what is the chance to select any one of the sample sizes? If the chances are equal, what type of sampling is this?

Answer 34

Possible samples: A, B A, C B, C There are three samples above, so equal chance for each would be 1/3 Simple random sample

Question 35

What is a simple random sample with replacement?

Answer 35

An individual can appear in the sample more than once

Question 36

What is a simple random sample without replacement?

Answer 36

An individual can appear in the sample AT MOST once

Question 37

If not particularly indicated in this course, does a simple random sample (SRS) occur with replacement or without?

Answer 37

Without replacement

Question 38

Consider a population containing 3 students, Anna, Bruce, and Cindy (ABC lol). All possible samples have a sample size n=2, if we use simple random sample with replacement, what are all the options?

Answer 38

A, A A, B A, C B, B B, C C, C

Question 39

What are some ways to obtain a simple random sample (SRS)?

Answer 39

By computer Random-number tables

Question 40

Assume that there are 500 residents in a community and we need to select a SRS with sample size 10. How do you use a random number table to randomly select the sample?

Answer 40

1. Number all residents from 1-500 2. Randomly pick a starting point from the random-number table. We look at the first 3 digits only as our biggest number (500) also has 3 digits. 3. Going from our starting point, we continue down the list selecting the first 10 numbers that are between 1-500

Question 41

Students were asked how much they liked their English class and options were: - Dislike very much - Dislike - Neutral - Like - Like very much What type of data is this?

Answer 41

Categorical ordinal

Question 42

What is best, a bar chart or pie chart, for categorical ordinal data?

Answer 42

The bar chart works nicely for ordinal data, as most people readily think from least to most (or lowest to highest) (or 1_dislike_very_much to 5_like_very_much). It requires a bit more cognitive work to move your mind among the outcomes (choices) of the categorical variable when we look at the pie chart.

Question 43

When looking at intervals for a histogram of continuous data, how do we denote cutpoints of the intervals and what does this mean? For example: Interval 1: 20 to under 30 Interval 2: 30 to under 40

Answer 43

[ means left end of data is closed (so the exact value) ) means the right end of the data is open (the up to part)

Question 44

You are building a histogram with the following intervals: [10,20), [20, 30), [30, 40), [40, 50), [50, 60) Which interval would 30 go into?

Answer 44

[30, 40) For [20, 30), it actually means up to 30, so 29.99999 would go in this bracket, but not 30

Question 45

What are the cutpoints for the interval [15, 20)?

Answer 45

15 and 20 Cutpoints are the values at the left (closed) and right (open) edges of each interval

Question 46

What is the midpoint for the interval [15, 20)?

Answer 46

17.5