H7.1

Suppose you find all the heights of the members of the​ men's basketball team at your school. Could you use those data to make inferences about heights of all men at your​ school? Why or why​ not?

One should not use these data to make inferences about heights of all men at the school because the sample is not random and is not representative of the population.

Suppose you want to estimate the mean GPA of all students at your school. You set up a table in the library asking for volunteers to tell you their GPAs. Do you think you would get a representative​ sample? Why or why​ not?

One would probably not get a representative sample because of response bias​ (students who volunteer will probably have higher GPAs than students who​ don't volunteer) and measurement bias​ (students may inflate their​ GPAs).

Is simple random sampling usually done with or without​ replacement?

Simple random sampling is usually done without​ replacement, which means that a subject cannot be selected for a sample more than once.

The mean GPA of all 3000 students at a college is 2.26. A sample of 100 GPAs from this school has a mean of 3.08. Which number is mu and which is x overbar​?

The population mean is =2.26​, and the sample mean is x =3.08.

A teacher at a community college sent out questionnaires to evaluate how well the administrators were doing their jobs. All teachers received​ questionnaires, but only​ 10% returned them. Most of the returned questionnaires contained negative comments about the administrators. Explain how an administrator could dismiss the negative findings of the report.

There is nonresponse bias. The results could be biased because the small percentage who chose to return the survey might be very different from the majority who did not return the survey.

A phone survey asked whether Social Security should be continued or abandoned immediately. Only landlines​ (not cell​ phones) were called. Do you think this would introduce​ bias? Explain.

This would likely introduce sampling bias because older people would be more likely to be surveyed than younger​ people, and older people are less likely to favor abandoning Social Security.

Assume your class has 30 students and you want a random sample of 10 of them. A student suggests asking each student to flip a​ coin, and if the coin comes up​ heads, then he or she is in your sample. Explain why this is not a good method.

this method is not good because it is unlikely to result in a sample size of 10.

When is a method called​ "biased"?

A biased method will tend to produce an untrue​ value, though not in every case.

Explain the difference between a parameter and a statistic.

A parameter is a measure of the​ population, such as the average height of everyone in a​ school, and a statistic is a measure of a​ sample, such as the average height of 5 people randomly selected in the same school.

What is a numerical value that characterizes some aspect of a​ population?

A parameter is a numerical value that characterizes some aspect of the population.

What is the term for a group of objects or people to be​ studied?

A population is a group of objects or people to be studied.

Explain the difference between a sample and a census. Every 10​ years, the U.S. Census Bureau takes a census. What does that​ mean?

A sample is a collection of people or objects taken from the population of interest. A census is a survey in which every member of the population is measured. When the U.S. Census Bureau takes a​ census, it conducts a survey of all people living in the U.S.

What is an important difference between statistics and​ parameters?

A statistic is a measurable estimator of an often unknown population parameter.

What are statistics sometimes​ called?

A statistic is sometimes called an estimator. A statistic is a numerical characteristic of a sample.

A researcher has designed a survey in which the questions asked do not produce a true answer. What is this an example​ of?

Measurement bias occurs when the method of data collection does not produce valid results.

You are receiving a large shipment of batteries and want to test their lifetimes. Explain why you would want to test a sample of batteries rather than the entire population.

If you test all the batteries to​ failure, you will not be able to sell any of them since none of them will work.

When reading about a​ survey, which of the following is important to​ know?

It is important to know whether there is nonreponse​ bias, which can be judged based on what percentage of people who were asked to participate actually did​ so, or voluntary response​ bias, which can be judged by whether the researchers chose people to participate in the survey or people themselves chose to participate.​ Therefore, it is important to know both A and B.

Explain the difference between sampling with replacement and sampling without replacement. Suppose you had the names of 10​ students, each written on a 3 by 5​ notecard, and want to select two names. Describe both procedures.

Describe sampling with replacement. Choose the correct answer below. Draw a​ notecard, note the​ name, replace the notecard and draw again. It is possible the same student could be picked twice. Describe sampling without replacement. Choose the correct answer below. Draw a​ notecard, note the​ name, do not replace the notecard and draw again. It is not possible the same student could be picked twice

To keep track of parameters and​ statistics, parameters are represented by Greek characters while statistics are represented by which of the​ following?

English letters are used to represent statistics.

You need to select a simple random sample of two from six friends who will participate in a survey. Assume the friends are numbered​ 1, 2,​ 3, 4,​ 5, and 6.

Friend 5 and friend 1