# Sophia Pathways Introduction to statistics Unit 1 Exam

Discipline: Statistics

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Question

Sophia Pathways Introduction to statistics Unit 1 Exam

(All Answers are in Bold Letters)

In 2007, 4% of people buying new cell phones purchased a bluetooth earpiece during the same transaction. In 2012, 28% of people buying new cell phones purchased a bluetooth earpiece during the same transaction.

Of the following choices, what is correct about the growth of bluetooth sales?

It rose by 12%.

It rose by 24%.

It rose by 120 percentage points.

It rose by 24 percentage points.

RATIONALE

We can note that the absolute difference between 2007 and 2012 is 4% to 28% or 24 percentage points.

To get the percent difference we take the absolute difference and divide by the initial value:

So we can say that sales actually grew 600%.

CONCEPT

Using Percentages in Statistics

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2

Jay wants to study nutrition and performance in schools using available data.

Which of the scenarios below will provide Jay with available data?

Going to a local high school and asking the principal for information about students' current and previous grades, then interviewing a random selection of students about their eating habits.

Going to a local high school and asking the principal for information about students' current and previous grades, then asking the health teacher for the results from a survey students took in health class.

Going to a local college and asking current undergraduates to report their grades and eating habits from high school.

Going to a local high school and asking the principal for information about students' previous grades, then interviewing a random selection of students about their eating habits.

RATIONALE

Recall, for data to be considered available data it must already be collected.  Since the grades data and survey data were already collected these are examples of available data.

CONCEPT

Data

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3

A pizza owner asked 50 customers to taste a new type of topping and found that 40 people liked its taste.

Which of these is an example of descriptive statistics?

80% of all people like the taste of the pizza topping.

80% of the surveyed customers like the taste of the pizza topping.

80% of all the pizza shop's customers like the taste of the pizza topping.

80% of the people in the city where the pizza shop is located like the taste of the pizza topping.

RATIONALE

Recall a descriptive statistic is a summary figure which uses the sample information at hand.  Using the sample information we know 40 of 50 people or 80% like the taste of the pizza topping.

CONCEPT

Statistics Overview

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4

Rob sent an email survey to 2,000 cell phone owners asking about their satisfaction with their current plan.  Only 256 people returned the survey and they were predominately 18-24 years old.

Which of the following statements is true?

Rob is ignoring the assumption that all survey participants will want to act independently.

Rob included too many people on the survey list, affecting the data collected.

The survey suffers from census issues because only 256 people responded.

The survey likely has bias because the people who could not answer differ from those who did answer.

RATIONALE

In this survey there was a very low response rate with only 256 of the 2000.  The characteristics of those who responded are different from non-responders.  Since the responders and non-responders differ, we would worry about this affecting how they responded.

CONCEPT

Bias

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5

Jessica uses a poorly calibrated stopwatch to note the finish time of a relay race. She noted the time as 125 seconds, whereas the actual time taken was 120 seconds.

The percent error in Jessica's calculation is __________.

4.2%

-4.2%

-4.0%

4.0%

RATIONALE

Recall that the percent error is equivalent to the absolute difference divided by the actual value.

If the actual measure is 120 seconds and  the observed measure is 125 seconds, then the absolute difference is:

So we calculate the percentage error to be:

CONCEPT

Absolute Change and Relative Change

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6

A grocery store owner asked the first 20 children who visited the store one day about their favorite snack.

This is what type of sampling?

Voluntary response sampling

Convenience sampling

Systematic sampling

Stratified sampling

RATIONALE

Recall that convenience samples are samples taken due to their ease of gathering information.  Since he simply asked the first 20 children, this is an example of that.  Convenience samples are generally biased as they probably don't represent the entire set of interest.

CONCEPT

Convenience & Self-Selected Samples

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7

The city government wants to conduct a survey on the number and types of cars owned by its residents.

How can the city use the cluster sampling method to find this information?

The city selects only those households that have more than one vehicle to complete the survey.

The city selects 100 households at random to complete the survey.

The city has every household within city limits complete the survey.

The city has every household in 10 neighborhoods complete the survey.

RATIONALE

Recall that clusters are generally geographic groups.  So, the city can put the neighborhoods into clusters and then choose a random sample of those clusters.

CONCEPT

Stratified Random and Cluster Sampling

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8

Nick designs a clinical trial to test a new anxiety medication by creating a control group and a treatment group. If he gives the medication to patients in the treatment group and not to the control group, some patients might find out that they're not being treated. To improve his study, Nick decides to give a sugar pill to the control group.

The sugar pill is an example of a __________.

confounding variable

variable of interest

placebo

case control

RATIONALE

When no active treatment is given to the control group, we refer to this as the placebo.

CONCEPT

Placebo

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9

To compare the teaching methodologies of two of its eighth-grade math teachers, a school decides to compare student test scores from the two classes throughout the year.

Which type of statistical study is the school conducting?

Matched-pair design study

Meta-analysis

Prospective observational study

Retrospective observational study

RATIONALE

A study which gathers data moving forward is called a prospective study.  Since the data is gathered on students without controlling the setting moving forward, it is a prospective observational design.

CONCEPT

Prospective and Retrospective Studies

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10

A researcher would like to determine which age groups (18-29, 30-49, 50-64, 65 or older) in the United States currently identify playing golf as their favorite pastime.

Which statistical study would be most appropriate to answer this question?

A single-blind experiment

A census

A prospective observational study

A survey

RATIONALE

In order to obtain information about favorite pastimes, it would be best to solicit information from people directly by using a survey.

CONCEPT

Surveys

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11

On a candy production line, 3% of bags are overfilled. An employee randomly selects 100 bags and finds that 5% are overfilled. A second employees takes another random sample of 250 bags and finds that 2% are overfilled.

Which of the following explains why there is a difference between the two percentages?

Random error; the numbers were different due to variability inherent in sampling.

The samples were not random samples.

The sample sizes were both too small, which is why they both obtained figures different than 3%

Both samples suffered from non-response bias.

RATIONALE

When sampling, there is always some variability that occurs.  So,

although the sample values are different from each other and the 3% true value, since they were randomly chosen, the differences are simply due to the variability that comes from sampling and not due to some systematic bias.  As the sample size would increase we would expect the variability to get smaller.

CONCEPT

Random and Systematic Errors

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12

Which of the following data types will be continuous?

The amount of snow that fell last night

The number of students who like chocolate or strawberry or vanilla ice-cream flavors

The number of books in the school library

RATIONALE

For data to be continuous, it must be able to take on any value inside of an interval.  The amount of snow that falls can be any value and is therefore continuous.  All the other measures can only take on a limited number of values.

CONCEPT

Discrete vs. Continuous Data

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13

In a bolt-manufacturing factory, it is estimated that 6% of the bolts being manufactured will be defective, with a 3% margin of error.

Choose the statement that correctly describes the confidence interval.

The percentage of defective bolts is between 3% and 6%.

The percentage of defective bolts is 6% or more.

The percentage of defective bolts is 6% or less.

The percentage of defective bolts is between 3% and 9%.

RATIONALE

Recall for a confidence interval, we take the point estimate +/- margin of error.  Using this framework we take the point estimate of 6%, then add and subtract the margin of error, 3%.

This gives us a CI of 3% to 9%.

CONCEPT

Margin of Error

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14

Select the correct statement regarding experiments.

A researcher can control the environment but cannot observe the response.

A researcher cannot control the environment but can observe the response.

A researcher can control the environment and observe the response.

A researcher can neither control the environment nor observe the response.

RATIONALE

The defining part of experimental setting is that the researcher can control the setting and apply some treatment to observe how it affects an outcome of interest.

CONCEPT

Observational Studies and Experiments

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15

Ben is measuring the effect that the potential energy of an object has on the height of an object's bounce

Which variable represents the height of an object's bounce?

Independent variable

Confounding variable

Explanatory variable

Response variable

RATIONALE

The outcome is the response, dependent or y -variable.  This is the height or bounce in this example.

CONCEPT

Variables

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16

The following shows the Consumer Price Index (CPI) for the years 2000-2005. All of the values use a reference year of 1983.

Which of the following is true about the CPI, based on the information?

\$100 in 1983 would be equivalent to \$189.70 in 2004.

\$100 in 2004 would have been worth 189.70 in 1983.

\$100 in 2002 would be equivalent to \$189.70 in 2004.

\$100 in 2000 would be equivalent to \$189.7 in 2004.

RATIONALE

Recall that the CPI allows us to transform values from some year to values in another year.  The value of the CPI in the base year is 100.  Since the CPI in 2004 is 189.7, this means that for \$100 in the base year of 1983 is equivalent to \$189.7 in 2004.

CONCEPT

Index Number and Reference Value

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17

A scientist is conducting a study on the effect of eating chocolate and overall mood. They believe that gender is a significant factor.  The participants are divided by gender.  Then, within each group, participants are randomly assigned to consume either chocolate or a placebo and then rate their mood for the day. This experiment will run for two weeks.

Which type of experimental design does this situation describe?

Randomized Block Design

Case-Control Design

Completely Randomized Design

Matched-Pair Design

RATIONALE

Since people are first divided by gender and then are assigned chocolate or placebo randomly, this is called a randomized block design.

CONCEPT

Randomized Block Design

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18

The owner of a new store on Main Street wants to turn the boulevard outside into extra parking spaces because she is concerned about parking availability. She randomly selects 500 residents of the town to take a survey, and these individuals have confirmed their participation. One of the survey questions reads, “Many residents believe the lack of available parking on Main Street is a major problem, and extra spaces along the boulevard would help. Do you agree?"

The store owner's survey could suffer from which type of bias?

Nonresponse bias

There is no evidence of bias in the way this survey is carried out.

Selection bias

Response bias

RATIONALE

By stating that many residents already believe parking is an issue and putting a response inside of the question, this is a good example of response bias.

CONCEPT

Nonresponse and Response Bias

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19

Scientists want to test a new pair of running shoes. A speed test is performed with two separate groups of participants. The treatment group will wear the new pair of running shoes, while the control group will not. It is believed that age and height may affect speed.

Which of the following would be most effective in controlling the confounding variables, such as age and height, in this study?

A matched-pair design experiment

A completely randomized design experiment

A retrospective observational study

A longitudinal observational study

RATIONALE

In order to control for variables that may affect the study, a matched pair design which matches as closely as possible for those variables would best control for their effects.

CONCEPT

Matched-Pair Design

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20

Choose the statement that accurately describes how a city government could apply systematic random sampling.

Every resident in five neighborhoods is selected to participate in a survey about city services.

Every resident is divided into groups, and 1,000 people are randomly selected to participate in a survey about city services.

Every individual over the age of 18 is selected to participate in a survey about city services.

Every fifth person in a population is selected to participate in a survey about city services.

RATIONALE

A systematic sample is when every nth element is chosen from the population.  In this case, by choosing every 5th household, this makes is a systematic sample.

CONCEPT

Simple Random and Systematic Random Sampling

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21

“Ugh,” Daniel says as he notices an office memo on his desk. It had been a fun weekend, and Monday morning came much too soon. He goes to the kitchen to refill his coffee mug. On the way, he runs into Sean, who asks, “How do you feel about the new office dress code?”

Which type of question has Sean asked?

Open question

Closed question

Closed and binomial question

Open and binomial question

RATIONALE

In an open question, a responder can answer how they like.  Since Sean can respond how he wants, this is an open question.

CONCEPT

Question Types

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22

Jenae is able to purchase a different brand of coffee for half the price from a new supplier. She anticipated that her co-workers would object to switching to the new brand, as they were really partial to the coffee they have been drinking so far. Indeed, when offered a taste test of the old brand versus the new brand, her co-workers unanimously rejected the new brand.

Jenae's boss, Steven, pointed out that this result was most likely due to the fact that the taste test was not ________.

controlled

randomized

blinded

replicated

RATIONALE

Since they didn't keep the participants unaware of what brand they were tasting, this could influence the findings.  So, the rejection of the new brand was likely due to not blinding them from what brand they were drinking.

CONCEPT

Blinding

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23

Which of these random samples represents a representative sample of the number of students in a middle school who walk to school?

5 students in the hallway

All students in chess club

150 random students at lunch

RATIONALE

For a sample to be representative it needs to look like the entire set of interest.  So, a random sample of all students at lunch will best represent the student population of interest.

CONCEPT

Random & Probability Sampling

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24

An insurance firm wants to estimate the percentage of senior citizens in a small town with approximately 2,534 residents. It asks a group of 85 randomly selected people in the town about their age.

Select the statement that is TRUE.

The sample is 85 people. The population is 2,449 people.

The sample is 85 people. The population is 2,534 people.

The sample is 2,534 people. The population is 85 people.

None of the answer choices are true.

RATIONALE

Recall the entire set of interest is the population and a sample is a subset of that population.  In this question the entire set is the 2534 residents, with the sample being the 85 that were chosen to be analyzed about their age.

CONCEPT

Sampling

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25

A university wants to survey its undergraduates about their satisfaction with the new website.  The university researchers pasted a link to the survey on the new website.  A majority of the surveys showed that students were happy with the new website and found it easy to use.  The university concluded that the website was fine and did not make any changes.

However, on Friday, hundreds of students turned up at the Undergraduate Student Committee meeting complaining about how difficult it was to navigate the new website. University researchers realized that placing the survey on the website meant that people who liked the website were more likely to access the survey.

Which of the following types of bias affected the survey's conclusions?

Selection bias

Deliberate bias

Response bias

Non-response bias

RATIONALE

Selection bias is when the mode of selection introduces a bias in the sample so that it is not representative of the population of interest.

Since they only collected information from those who used the website, this does not represent how students in

general feel about the website and is therefore an example of selection bias.

CONCEPT

Selection and Deliberate Bias

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26

Jenae changed the original coffee labels with plain white ones that had the flavor printed in bold black letters, and she placed them on the coffee pots for the week-long experiment.

Jenae used an aspect of experimental design known as ________ when she created the labels to have the same appearance.

replication

randomization

a control

a treatment

RATIONALE

In an experiment, controls are when conditions are manipulated by the experimenter to keep conditions as consistent as possible.  When Jenae makes the labels the same the entire week, this is an example of a control.

CONCEPT

Experimental Design

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27

A local gym conducts a survey among the people in a mall.

Which survey question would have a qualitative response?

How many servings of fruits do you eat every day?

How much do you weigh, in pounds?

What is the amount of weight you can bench press, in pounds?

Do you exercise daily?

RATIONALE

Simply stating yes or no is simply descriptive and cannot be measured numerically or used in arithmetic, so it is qualitative.

CONCEPT

Qualitative and Quantitative Data

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28

To test the effectiveness of a new, cholesterol-lowering drug, a group of researchers recruits 200 volunteers with high cholesterol to take part in a study. The researchers place the numbers 1 through 200 in a hat and have each participant select a number. Those who picked an odd number receive the new drug, while those who picked an even number receive a placebo.

Which experimental design are the researchers using?

Completely Randomized Design

Matched-Pair Design

Randomized Block Design

Representative Sample Design

RATIONALE

When all patients are assigned treatment or control randomly without considering other factors, this is called a completely randomized design.

CONCEPT

Completely Randomized Design

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29

A hunter is practicing his aim using a practice target. He takes 5 shots. All 5 shots hit the target, but they do not hit or surround the bullseye. In addition, all 5 shots are very spread apart on the target.

Classify the hunter's accuracy and precision.

High accuracy and low precision

Low accuracy and low precision

Low accuracy and high precision

High accuracy and high precision

RATIONALE

Since the arrows fall away from the bullseye and are spread out we would classify this as low accuracy and low precision.
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