Stats 115 Chapter 1-12 Midterm

Statistics

Characteristic of a sample

An electronics store receives a shipment of eight boxes of calculators. Each box contains ten calculators. A quality control inspector chooses a box by putting eight identical slips of paper numbered 1 to 8 into a hat, mixing thoroughly and then picking a slip at random. He then chooses a calculator at random from the box selected using a similar method with ten slips of paper in a hat. He repeats the process until he obtains a sample of 5 calculators for quality control testing. Does this sampling plan result in a random sample? Simple random sample? Explain. A) No; yes. The sample is not random because not all calculators have the same chance of being selected. It is a simple random sample because all samples of 5 calculators have the same chance of being selected. B) Yes; no. The sample is random because all calculators have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample containing 5 calculators from the same box. C) No; no. The sample is not random because not all calculators have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample containing 5 calculators from the same box. D) Yes; yes. The sample is random because all calculators have the same chance of being selected. It is a simple random sample because all samples of 5 calculators have the same chance of being selected.

D) Yes; yes. The sample is random because all calculators have the same chance of being selected. It is a simple random sample because all samples of 5 calculators have the same chance of being selected.

13

Find the variance of the following sample of numbers: 2, 7, 9

Double Blindness

Forty people were randomly chosen to participate in an experiment to determine if a new drug reduces cholesterol. Twenty people received the new drug treatment, while the remaining twenty received a placebo. Neither the patients nor the doctors administering the treatment knew if the patient was receiving the placebo or the drug treatment. This is an example of:

1.6

In April 2011, the Gallup Poll asked a random sample of 1077 adults, People feel differently about how far a government should go. Here is a phrase which some people believe in and some don't. Do you think our government should or should not redistribute wealth by heavy taxes on the rich? It found that 47% said our government should redistribute wealth by heavy taxes on the rich. Suppose that the sample size had been 4000 rather than 1077. Find the margin of error for 95% confidence in this case. Answer in percents using one decimal place. 1.5,1.6,1.9,3.9

Quantitative Variables (Numerical)

Information that can be measured and written down with numbers.

Large samples give ____ variable results as compared to smaller samples.

Less

Survey

Measures the entire target population is called a census

Explanatory Variable

One that explains changes in that variable (independent)

The error that arises as a result of taking a sample from a population rather than using the whole population

What is a sampling error ?

.Non response

When you take the number of the people in the survey and dive the number of respondents by it and then subtract that number by 100.

Experiments

Which of the following types of studies can have treatments?

The key(s) to a convincing experiment is/are: -Adequate number of subjects -Control -Randomization -All of the choices are correct.

-All of the choices are correct.

Principles of an experimental design

1. Control 2. Randomize 3. Use enough subjects

A November 2011 Gallup Poll of 1012 adults found that 607 are satisfied with the total cost they pay for their health care. The announced margin of error is ±4 percentage points. The announced confidence level is 95%. Fill in the blank: The value of the sample proportion who say they are satisfied with the total cost they pay for their health care is ___%. 15%, 55%, 58%, 60%

60

What is the effect of word bias in a survey?

A biased survey is one that encompasses errors caused by the design of the survey and its questions. It's important for you, the survey creator, to create survey questions that don't change the survey outcome. Things to consider are the way questions are worded, the structure of the survey and even its design, style and colors. A biased survey can lead to survey response bias and higher than normal drop-out rates.

Any number of explanatory variables

A completely randomized design can have:

Observational Study

A marketing firm does a survey to find out how many people use a product. Of the one hundred people contacted, fifteen said they use the product. A) Experiment B) Observational study

Experiment

A quality control specialist compares the output from a machine with a new lubricant to the output of machines with the old lubricant. A) Observational study B) Experiment

Bias sample

A sample is collected in such a way that some members of the intended population are less likely to be included than others.

Census

A study of every unit, everyone or everything, in a population

Simple Random Sample

A subset of a statistical population in which each member of the subset has an equal probability of being chosen.

Lurking

A variable that has an important effect on the relationship among the variables in a study but is not one of the explanatory variables studied.

Voluntary Response Sample

Bias occurs when sample members are self-selected volunteers

Parameter

Characteristic of a population.

Can aspirin help prevent heart attacks? The Physicians' Health Study, a large medical experiment involving 22,000 male physicians, attempted to answer this question. One group of about 11,000 physicians took an aspirin every second day, while the rest took a placebo. After several years, the study found that subjects in the aspirin group had significantly fewer heart attacks than subjects in the placebo group. Match the terms used in experiments with their corresponding values in view of the given study.

Explanatory- medication Response- health Subject- physician

A New York Times article reported that average Math SAT scores for the high school class of 2007 dropped 3 points compared with scores in 2006. Officials of the College Board, the nonprofit organization that administers the SAT, suggested that increased numbers of students taking the SAT had contributed to the decline in scores. "The larger the population you get that takes the exam, it obviously knocks down the scores," said Gaston Caperton, the president of the College Board. True or false: The conclusion is the result of an experiment with explanatory variable number of students taking the exam and response variable average Math SAT score.

False

A carload lot of ball bearings has an average diameter of 2.503 centimeters (cm). This is within the specifications for acceptance of the lot by the purchaser. The inspector happens to inspect 100 bearings from the lot with an average diameter of 2.515 cm. This is outside the specified limits, so the lot is mistakenly rejected.

Parameter- 2.503 Statistic- 2.515 Sample- 100

A student is interested in determining if the cost of a textbook depends on the number of pages. The student goes to the campus bookstore, picks a textbook rack at random, and records the number of pages and price of each textbook on the rack. What is the population in this study? What is the sample? What variables does the student measure?

Population- textbooks Sample- all books on the shelf Variables- number of pages

Pregnant and breast-feeding women should eat at least 12 ounces of fish and seafood per week to ensure their babies' optimal brain development, according to a coalition of top scientists from private groups and federal agencies. A nutritionist wants to know whether pregnant women are eating at least 12 ounces of fish per week. To do so, she obtains a list of the 340 members of a local chain of prenatal fitness clubs and mails a questionnaire to 60 of these women selected at random. Only 21 questionnaires are returned. Which of the following is the population in this study? Pregnant breast feeding woman, Private groups and federal agencies, members of fitness club

Pregnant breast feeding woman

Students in a large statistics class were randomly divided into two groups. The first group took the midterm exam in the morning with a symphony by Mozart playing in the background while the second group took the exam in the afternoon with rock music playing. The scores of the two groups on the exam were compared. This study is a(n)

Randomized comparative experiment

Seasonally Adjusted Data

Removing the seasonal component of a time series that exhibits a seasonal pattern.

In examining a relationship between two variables, the variable we think represents the outcome of interest is called the ________________ variable.

Response

Do doctors in managed care plans give less charity care? Researchers chose 60 communities at random, then chose doctors at random in each community. In all, they interviewed 10,881 doctors. Overall, 77.3% of the doctors said they had given some care free or at reduced rates because of the patient's financial need in the month before the interview. Doctors who received at least 85% of their practice income from managed care plans were significantly less likely than other doctors to provide charity care. This study is a(n)

Sample survey

Median is greater than the mean(tailed left)

Skewed left

Mean is greater than the median(tailed right)

Skewed right

A poll of 1700 randomly selected students in grades 6 through 8 was conducted and found that 37% enjoy playing sports. Is the 37% result a statistic or a parameter? Explain.

Statistic, because it is calculated from a sample, not a population.

Qualitative Variables (categorical)

Variables with no natural sense of ordering. They are therefore measured on a nominal scale. For instance, hair color (Black, Brown, Gray, Red, Yellow)

Mean, median, and mode fall in the same place

Symmetric distribution

The placebo effect

The drug manufacturer Merck recently stopped testing a promising new drug to treat depression. It turned out that in a randomized, double-blind trial a dummy pill did almost as well as the new drug. The fact that many people respond to a dummy treatment is called

Response Variable

The focus of a question in a study or experiment (dependent)

Margin of Error

The range of values below and above the sample statistic in a confidence interval.

Variability

The range, the interquartile range (IQR), variance, and standard deviation

Completely randomized experimental design

The simplest statistical design for an experiment is a(n):

Confounding

To variables are said to be this when their effects on a response variable cannot be distinguished from each other.