Final

Explain why the term​ APR/n appears in the compound interest formula for interest paid n times a year.

APR represents the annual percentage rate​ (as a​ decimal). To account for the interest paid n times a​ year, this annual​ (yearly) rate needs to be divided by the number of compounding periods per​ year, n.

population parameter

specific numbers of interest to researchers that describe certain characteristics of the population

Statistics

the science of collecting, organizing, and interpreting data

Each​ year, a group surveys​ 50,000 households to study internet usage. In one area of the​ study, the group is interested in finding out how many hours a day the household spends streaming video from the internet. Describe the five basic steps in a statistical study with an example of their application below.

1.State the goal of your study. In this​ case, it is to discover how many hours per day a household spends streaming internet video. 2.Choose a representative sample from the population. In this​ case, it would be choosing a sample of​ 50,000 households. 3.Collect raw data from the sample and summarize these data by finding sample statistics of interest. In this​ case, it would be asking the households how many hours they spend streaming internet video and turning this data into an average. 4.Use the sample statistics to infer the population parameters. In this​ case, based on the data​ gathered, the group estimates the average time per day that a household spends streaming internet video. 5.Draw conclusions to determine what you learned and whether you achieved your goal. In this​ case, we discovered the average time per day that a household spends streaming internet video.

Eight guidelines for evaluating a statistical study

Eight Guidelines for Evaluating a Statistical Study 1. Get a Big Picture View of the Study. You should understand the goal of the study, the population that was under study, and whether the study was observational or an experiment. 2. Consider the Source. Look for potential sources of bias on the part of the researchers. 3. Look for Bias in the Sample. Decide whether the sampling method was likely to produce a representative sample. 4. Look for Problems in Defining or Measuring the Variables of Interest. Ambiguity in the variables can make it difficult to interpret reported results. 5. Beware of Confounding Variables. If the study neglected potential confounding variables, its results may not be valid. 6. Consider the Setting and Wording in Surveys. Look for anything that might tend to produce inaccurate or dishonest responses. 7. Check That Results Are Presented Fairly. Check whether the study supports the conclusions that are presented in the media. 8. Stand Back and Consider the Conclusions. Evaluate whether the study achieved its goals. If so, do the conclusions make sense and have practical significance?

Describe and contrast selection bias and participation bias in sampling.

Selection bias occurs whenever researchers select their sample in a biased way. Participation bias occurs any time participation in a study is voluntary.

What is the difference between simple interest and compound​ interest? Why do you end up with more money with compound​ interest?

Simple interest is interest paid only on the original investment whereas compound interest is interest paid both on the original investment and on all interest that has been added to the original investment. Since compound interest is calculated based on a larger amount than simple​ interest, it results in a larger amount of money over time.

Define the terms​ population, population​ parameter, sample, raw​ data, and sample statistic as they apply to statistical studies

The population is the complete set of people or things being studied, a population parameter is a number that describes a characteristic of the​ population, a sample is the set of people or things from which the data are obtained, a sample statistic is a number that describes a characteristic of a​ sample, and raw data are the individual measurements collected.

Give an example of a situation in which you might want to solve the savings plan formula to find the​ payments, PMT, required to achieve some goal.

A parent wants to build a​ $100,000 college fund in 18 years by making​ regular, end-of-month deposits.

What is an installment​ loan? Explain the meaning and use of the loan payment formula.

An installment loan is a loan that is paid off with equal regular payments. The loan payment formula is used to calculate equal monthly payments as the interest paid decreases and principal decreases.

Give an example. Choose the correct answer below. 4cont

D. An investor has a starting principal P=​$3000 and an accumulated value of A=​$8400 after Y=4 years. The annual return is annual return=AP1/Y−1=$8400$30001/4−1=42.8−1≈0.294=29.4%.

how the portions of loan payments going to principal and interest change over the life of the loan.

Installment loans gradually pay down the loan principal while the payments remain the same.​ Therefore, the interest due each month gradually decreases and the amount paid toward the principal gradually increases.

population

in a statistical study is the complete set of people being studied

Briefly describe each of the eight guidelines for evaluating statistical studies. Describe how each would apply to a statistical study in which researchers are looking to discover what breed of dog sleeps the most.

1. Get a big picture view of the study. In the example​ study, the goal is to discover sleeping habits in a population of dogs with an observational study. 2. Consider the source. In the example​ study, the veterinarians have no preference on which breed gets the most sleep. 3. Look for bias in the sample. In the example​ study, all breeds were given appropriate sleeping quarters. 4.Look for problems in defining or measuring the variables of interest. In the example​ study, sleep is strictly measured according to set guidelines. 5.Beware of confounding variables. In the example​ study, the researchers gave the dogs the same amout of activity before letting them sleep. 6.Consider the setting and wording in surveys. In the example​ study, the researchers phrased the sleep data in clear wording 7.Check that results are presented fairly. In the example​ study, the data supports the breed that the researchers claim sleeps the most. 8.Stand back and consider the conclusions. In the example​ study, the researchers achieved their goal of finding which breed of dog sleeps the most.

Steps 1-5 of statistics

Basic Steps in a Statistical Study 1. State the goals of your study. That is, determine the population you want to study and exactly what you'd like to learn about it. 2. Choose a representative sample from the population. 3. Collect raw data from the sample and summarize these data by finding sample statistics of interest. 4. Use the sample statistics to infer the population parameters. 5. Draw conclusions: Determine what you learned and how it addresses your goals

Representative sample

Sample in which the relevant characteristics of the sample members are generally the same as those of the population

Sample

Subset of the population which raw data is actually obtained

What do we mean by variables of interest in a​ study?

The items or quantities that the study seeks to measure

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. I followed all the guidelines for sample selection​ carefully, but my sample still did not reflect the characteristics of the population.

The statement makes sense because even if a sample is chosen in the best possible​ way, it may not be representative of the population by random chance.

Distinguish between the total return and the annual return on an investment. How do you calculate the annual​ return? Choose the correct answer below.

The total return is the percentage change in the investment value. The annual return is the annual percentage yield​ (APY) that would give the same overall growth over Y years. The formula is annual return=AP(1/Y)−1.

sample statistic

nu,bers decribing characteristics of the sampl, found by consolidating or summarizing the raw data collected from the sample