Math 121 Chapter 7

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 7000 students at a college is 2.83. A sample of 100 GPAs from this school has a mean of 3.06. Which number is mu and which is x overbar​?

The population mean is muequals2.83​, and the sample mean is x overbarequals3.06.

Suppose​ that, when taking a random sample of three​ students' GPAs, you get a sample mean of 3.90. This sample mean is far higher than the​ college-wide (population) mean. Does this provide that your sample is​ biased? Explain. What else could have caused this high​ mean?

The sample may not be biased. The high mean might have occurred by​ chance, since the sample size is very small.

A random sample of likely voters showed that 62​% planned to vote for Candidate​ X, with a margin of error of 4 percentage points and with​ 95% confidence. b. Is there evidence that Candidate X could​ lose?

There is no evidence that the candidate could lose. The reason there is no evidence is because the interval is entirely above​ 50%.

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.

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.

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.

Explain the difference between a parameter and a statistic.

A parameter is a measure of the​ population, and a statistic is a measure of a sample.

A random sample of likely voters showed that 62​% planned to vote for Candidate​ X, with a margin of error of 4 percentage points and with​ 95% confidence. c. Suppose the survey was taken on the streets of a particular city and the candidate was running for president of the country that city is in. Explain how that would affect your conclusion.

A sample from this particular city would not be representative of the entire country and would be worthless in this context.

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.

Suppose you attend a school that offers both traditional courses and online courses. You want to know the average age of all the students. You walk around campus asking those students that you meet how old they are. Would this result in an unbiased​ sample?

No, since this method will not select people who take online classes but may have a different mean age than the traditional students.

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 would have no batteries to sell.

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 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.

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.

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. Use the line from a random number table shown below to select your sample. Start from the left. 0 5 8 5 7 8 1 4 9 9 7 2 4 3 5 2 1 1 0 6 7 5 5 1

Friend 5 and friend 1

A random sample of likely voters showed that 62​% planned to vote for Candidate​ X, with a margin of error of 4 percentage points and with​ 95% confidence. a. Use a carefully worded sentence to report the​ 95% confidence interval for the percentage of voters who plan to vote for Candidate X.

I am​ 95% confident that the population percentage of voters supporting Candidate X is between 58​% and 66​%.