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Chapter 7: Q. 7 (page 454)

Refer to the small population of 5students in the table.

Sample means List all 10 possible SRSs of size n=2, calculate the

mean quiz score for each sample, and display the sampling distribution of the sample

mean on a dotplot.

Short Answer

Expert verified

Answer to the given question:

Sample of size2Sample mean
Abigail-Bobby7.5
Abigail-Carlos10
Abigail-DeAnna8.5
Abigail-Emily9.5
Bobby-Carlos7.5
Bobby-DeAnna6
Bobby-Emily7
Carlos-DeAnna8.5
Carlos-Emily9.5
DeAnna-Emily8

Dotplot:

Step by step solution

01

Given information

Sample of size 2GenderQuiz score
AbigailMale10
BobbyFemale5
CarlosFemale10
DeAnnaMale7
EmilyMale9
02

Explanation

All the possible samples of size 2then contain any two (different) people of the population of 5students.

Sample of size2
Abigail-Bobby
Abigail-Carlos
Abigail-DeAnna
Abigail-Emily
Bobby-Carlos
Bobby-DeAnna
Bobby-Emily
Carlos-DeAnna
Carlos-Emily
DeAnna-Emily

The sample mean of a sample is then the sum of the two corresponding quiz scores divided by the number of data values.

Sample of size2Sample mean
Abigail-Bobbyx¯=10+52=152=7.5
Abigail-Carlosx¯=10+102=202=10
Abigail-DeAnnax¯=10+72=172=8.5
Abigail-Emilyx¯=10+92=192=9.5
Bobby-Carlosx¯=5+102=152=7.5
Bobby-DeAnnax¯=5+72=122=6
Bobby-Emilyx¯=5+92=142=7
Carlos-DeAnnax¯=10+72=172=8.5
Carlos-Emilyx¯=10+92=192=9.5
DeAnna-Emilyx¯=7+92=162=8

Dotplot:

Create a number line

For every given data value place a dot above the corresponding number on the number line.

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Most popular questions from this chapter

The number of unbroken charcoal briquets in a 20-pound bag filled at the factory follows a Normal distribution with a mean of 450 briquets and a standard deviation of 20 briquets. The company expects that a certain number of the bags will be underfilled, so the company will replace for free the 5%of bags that have too few briquets. What is

the minimum number of unbroken briquets the bag would have to contain for the company to avoid having to replace the bag for free?

a. 404

b. 411

c. 418

d. 425

e. 448

Iced tea On Tuesday, the bottles of Arizona Iced Tea filled in a plant were supposed to contain an average of 20ounces of iced tea. Quality control inspectors selected 50bottles at random from the day’s production. These bottles contained an average of 19.6 ounces of iced tea. Identify the population, the parameter, the sample, and the statistic.

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.

Detecting gypsy moths The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed with a mean of 0.5 and a standard deviation of 0.7.

a. Explain why it is reasonable to use a Normal distribution to approximate the sampling distribution of x-x¯for SRSs of size 50 .

b. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

c. In a recent month, the mean number of moths in an SRS of size 50 was x-=0.6. x¯=0.6. Based on this result, is there convincing evidence that the moth population is getting larger in this state? Explain your reasoning.

A 10-question multiple-choice exam offers 5 choices for each question. Jason just guesses the answers, so he has probability 15of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. What would be a proper way to use a table of random digits to do this?

a. One digit from the random digit table simulates one answer, with 5 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers.

b. One digit from the random digit table simulates one answer, with 0 or 1 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers.

c. One digit from the random digit table simulates one answer, with odd = correct and even = incorrect. Ten digits from the table simulate 10 answers.

d. One digit from the random digit table simulates one answer, with 0 or 1 = correct and all other digits = incorrect, ignoring repeats. Ten digits from the table simulate 10 answers.

e. Two digits from the random digit table simulate one answer, with 00 to 20 = correct and 21 to 99 = incorrect. Ten pairs of digits from the table simulate 10 answers.
See all solutions

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