# SOPHIA PATHWAYS Introduction to Statistics Milestone 1

**Discipline:** Statistics

**Type of Paper:** Creative writing

**Academic Level:** High school

**Paper Format:** APA

**Pages:**1

**Words:**275

Question

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?

## RATIONALE

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

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?**

## RATIONALE

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

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.

## 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%.

Rachel, a professional bean bag athlete, throws three bean bags, aiming for the hole in the wooden board. However, her throws result in the bags spread out across the board as shown.

Which of the following best classifies the arrangement of bean bags?

## RATIONALE

The bean bags are not close to the hole and they are spread out. So they are not accurate or precise or we can say low accuracy and precision.

A factory manufactures bolts. One of its employees, working in the quality control department, checks the first 20 bolts manufactured in a day for possible defects.

**This is what type of sampling?**

## RATIONALE

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

Jenae noticed that many of her co-workers would opt for the coffee that appeared to be most recently brewed, regardless of the flavor of the coffee offered. This leads her to believe that what she was witnessing was not really representative of everyone's true flavor preferences. She adapted her experimental study accordingly.

**Select one control in Jenae's experimental study.**

## RATIONALE

In an experiment, controls are when conditions are manipulated by the experimenter to keep conditions as consistent as possible. In this example Jenae brews coffee at the same time, so this is a control.

**Which of these random samples represents a representative sample of the systolic blood pressure of all patients in a hospital?**

## RATIONALE

For a sample to be representative it needs to look like the entire set of interest. To look like all patients in the hospital, they should be randomly sampled from the entire population not simply the neurology department or children. Employees are not a part of the population of interest.

**Select the correct statement regarding experiments.**

## 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.

An appliance store manager noted that the sales of home appliances contributed 74% of the store's profits in the year 2010 and 82% in the year 2011.

**Of the following choices, which two statements about home appliance sales are true?**

## RATIONALE

We can note that the absolute difference between 2010 and 2011 is 74% to 82% or 8 percentage points.

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

So we can say sales actually grew by 10.8%.

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?**

## 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.

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?**

## RATIONALE

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

**Which of the following data types will be continuous? **

## RATIONALE

The total weight of apples can take on any value and is therefore continuous. The other measures can only take on a limited number of values and are discrete.

Mike wants to find out the approximate income for professors in Michigan. He decides to randomly select 50 professors who work for a college or university in Michigan and obtain their salaries.

**What are the sample and the population of Mike's study?**

## 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 are all the professors at a university or college in Michigan, with the sample being the 50 that were chosen to be analyzed about their salary.

A different coffee seller offered to sell coffee to Jenae's company for half the cost of their current brand. Jenae knew her co-workers were really partial to the coffee they drank now, so she decided to conduct a study to see if they noticed the difference in flavor. Her co-workers were convinced they would.

Jenae provided each person with a sample and said that some had the new coffee and some did not. Only Jenae knew who had which brand of coffee.

**Jenae's strategy is an example of a(n) ________.**

## RATIONALE

Since participants are unaware of what group they are in, regular or new coffee group, this is referred to as blinding in an experiment.

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?

## RATIONALE

Recall the CPI gives us a measure of price changes over time and allows us to transform values in one year to another. The value of the CPI in the base year is 100. This means that for $100 in 1983 is equivalent to $178 in 2001.

A retail brand plans to open its stores across all cities with a population of more than one million. To prepare for this, it refers to the past year's census done by the government.

**Which statement accurately describes the type of data the retail brand is using?**

## RATIONALE

Since the retailer doesn't gather the data itself, but relies upon data that has already been collected, this is an example of using available data.

The manager of a food company wants to conduct a survey to find out whether consumers like or dislike a new brand of soup that was recently launched.

**Which of the following data collection methods is mostly likely to get unbiased results?**

## RATIONALE

In order to get the best understanding of which soup is the most popular, they want to get a sense of what brands in general customers like. By asking customers from all around the state will better capture responses in general than simply asking those who are near the company headquarters or those who live near the manager.

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?**

## 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.

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?**

## 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.

In a study to assess the risk of obesity with the amount of time exercised per week, researchers matched each patient, in a sample of 500 people who are obese, with a person of the same ethnicity, gender, and age (along with other similar characteristics) who is not obese. The researchers asked the patients and their matches a series of questions, and then tracked eating and exercise habits regularly for several years.

**Which type of statistical study are the researchers conducting?**

## RATIONALE

Since the study collected information on people over several years moving forward, it is a prospective study design.

A local bakery conducts a phone survey to find the most popular types of cakes. They selected 100 random phone numbers from the local telephone directory and called them.

**This type of sampling method is called __________.**

## RATIONALE

~~By choosing randomly from the directory, all people should have an equal chance of being chosen. This would make it a simple random sample.~~

Melissa is conducting a survey of her classmates because her teacher wants the class to learn more about hygiene habits. Melissa has developed a list of 10 questions. “Do you brush your teeth every day?” is the first question she asks.

**Which type of question is Melissa asking? **

## RATIONALE

In this question, the responses are limited and there are only 2 responses. This would be a closed binomial question type.

Jenae's study ignored the fact that only some of her coffee choices had caffeine, even though her co-workers preferred caffeinated coffee. Therefore, Jenae decided to label one type of decaffeinated coffee as having caffeine to see what would happen.

As she anticipated, this coffee became more popular with her co-workers, and they claimed that the extra boost of caffeine helped them focus on their work.

**The growing popularity of the decaffeinated coffee among co-workers, under the false impression that it gave them extra caffeine, is an example of ________.**

## RATIONALE

Since no treatment of caffeine was given to these participants in the control group and they reported an effect, this is what we refer to as the placebo effect.

Cindy measured and recorded the temperature of a liquid for an experiment. She used a poorly calibrated thermometer and noted the temperature as 100.5 degrees Fahrenheit. The actual temperature of the liquid was 95 degrees Fahrenheit.

**The percent error in her calculation is __________.**

## RATIONALE

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

If the absolute measure is 95 degrees and the observed measure is 100.5 degrees, then the absolute error is:

So we calculate the percentage error to be:

A sports trainer is going to do an experiment on the effect of Vitamin D supplements and his athletes. He randomly assigns all of his patients to either take Vitamin D supplements or take a placebo.

**What type of experimental design does this situation illustrate?**

## RATIONALE

Since all athletes are assigned treatment or control for vitamin D randomly without considering other factors, this is called a completely randomized design.

The manager of an amusement park conducts a survey among the people visiting the park to learn their favorite rides. Out of 100 people randomly selected to complete the survey, 25 people have chosen not to participate.

**The manager's survey suffers from which of the following types of bias?**

## RATIONALE

Since 25% of the people didn't respond to the survey, we would worry about nonresponse bias, which means those who didn't respond would produce a very different outcome than those who did respond.

A travel agency contacted a department store and obtained the list of all people who made purchases using their credit cards at the store in the last month. The agency then surveyed a random sample from the list, calling them to ask their preference for air travel or train travel for taking holidays.

**Which of the following types of bias affects the conclusions of the survey?**

## 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 using their credit card at a department store, this does not represent how people travel in general and is therefore an example of selection bias.

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?**

## 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.

A survey conducted among students in the school cafeteria asked a set of questions listed below.

**Which survey question would produce a qualitative response? **

## RATIONALE

Qualitative data only describes and cannot be used in arithmetic. A person's favorite dish can only be measured descriptively and is therefore qualitative