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Chapter 8: Q 66. (page 542)

Check them all Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.

a. We want to estimate the average age at which U.S. presidents have died. So we obtain a list of all U.S. presidents who have died and their ages at death.

b. Do teens text more than they call? To find out, an AP Statistics class at a large high school collected data on the number of text messages and calls sent or received by each of 25randomly selected students. The boxplot displays the difference (Texts 鈭� Calls) for each student.

Short Answer

Expert verified

a. The conditions not met are: Random Sample and Independent.

b. Condition not met is of Large Sample.

Step by step solution

01

Part (a) Step 1: Given Information

It is given that population is taken of all US president.

02

Part (a) Step 2: Explanation

Conditions are:

  • Random: In sample, all US president are included. It cannot be random sample.
  • Independence: Sample of US presidents can never be less than 10%of total population of US president.
  • Large Sample Size: It will be >30as they are for sure more than 30

The conditions not met are: Random Sample and Independent.

03

Part (b) Step 1: Given Information

It is given that n=25

Population is of all the students.

04

Part (b) Step 2: Explanation

Conditions are:

  • Random: This is satisfied as students are selected randomly.
  • Independent: 25<10%of population of all students.
  • Large Sample Size: 25<30. This is not met.

Condition of Large Sample is not met.

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Most popular questions from this chapter

Selling online According to a recent Pew Research Center report, many

American adults have made money by selling something online. In a random sample of 4579American adults, 914reported that they earned money by selling something online in the previous year. Assume the conditions for inference are met.

Determine the critical value z* for a 98% confidence interval for a proportion.

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would report having earned money by selling something online in the previous year.

c. Interpret the interval from part (b).

A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: 鈥淒o you think that the drinking age should be reduced to eighteen in light of the fact that 18-year-olds are eligible for military service?鈥� He asks listeners to go to his website and vote 鈥淵es鈥� if they agree the drinking age should be lowered and 鈥淣o鈥� if not. Of the 100 people who voted, 70 answered 鈥淵es.鈥� Which of the following conditions are violated?

I. Random

II. 10%

III. Large Counts

a. I only

b. II only

c. III only

d. I and II only

e. I, II, and III

You have an SRS of 23observations from a large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98%confidence interval for the mean of the population?

a. 2.177

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d. 2.500

e. 2.508

Most people can roll their tongues, but many can鈥檛. The ability to roll the tongue is

genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400students and find that 317can roll their tongues. The margin of error for a 95%confidence interval for the true proportion of tongue rollers among students is closest to which of the following?

a. 0.0008

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t time When constructing confidence intervals for a population mean, we almost always use critical values from a t distribution rather than the standard Normal distribution.

a. When is it necessary to use a t critical value rather than a z critical value when constructing a confidence interval for a population means?

b. For a particular level of confidence, explain what happens to the t critical values as Page Number: 548 the degrees of freedom increase.
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