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The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset Vaia Explanations$ Math

4th Edition · 809 pages

ISBN: 9781319113339

Chapter 10: Q. 40 (page 652)

40. Household size How do the numbers of people living in households in the United Kingdom (U.K.) and South Africa compare? To help answer this question, we used Census At School’s random data selector to choose independent samples of $50$ students from each country. Here is a Fathom dotplot of the household sizes reported by the students in the survey.

Short Answer

Expert verified

All requirements (Random, Normal, and Independent) have been met.

Step by step solution

01

Given information

A School’s random data selector to choose independent samples of $50$ students from each country.

02

Explanation

Random, Normal, and Independent are the requirements for two-sample t methods.

Random: Because the data was obtained, utilizing the random data selector, which is satisfied.
Normal: Satisfied, that both samples $(50)$ have a sample size of at least $30$ .
Independent: Satisfied since the samples are independent and the sample size is less than 10% of the total population size.
As a result, all conditions have been met.

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Most popular questions from this chapter

The elderly fear crime more than younger people, even though they are less likely to be victims of crime. One study recruited separate random samples of $56$ black women and $63$ black men over the age of $65$ from Atlantic City, New Jersey. Of the women, $27$ said they “felt vulnerable” to crime; $46$ of the men said this.

(a) Construct and interpret a $90 %$ confidence interval for the difference in population proportions (men minus women).

(b) Does your interval from part (a) give convincing evidence of a difference between the population proportions? Explain.

Computer gaming Do experienced computer game players earn higher scores when they play with someone present to cheer them on or when they play alone? Fifty teenagers who are experienced at playing a particular computer game have volunteered for a study . We randomly assign $25$ of them to play the game alone and the other $25$ to play the game with a supporter present. Each player’s score is recorded.

(a) Is this a problem with comparing means or comparing proportions? Explain.

(b) What type of study design is being used to produce data?

In an experiment to learn whether Substance M can help restore memory, the brains of $20$ rats were treated to damage their memories. The rats were trained to run a maze. After a day, $10$ rats (determined at random) were given M and $7$ of them succeeded in the maze. Only $2$ of the $10$ control rats were successful. The two-sample z test for “no difference” against “a significantly higher proportion of the M group succeeds”

(a) gives $z = 2.25, P < 0.02$

(b) gives $z = 2.60, P < 0.005$

(c) gives $z = 2.25, P < 0.04$ but not $< 0.02$

(d) should not be used because the Random condition is violated

(e) should not be used because the Normal condition is violated.

Explain why the conditions for using two-sample z procedures to perform inference about $p 1 - p 2$ are not met in the settings

Don’t drink the water! The movie A Civil Action (Touchstone Pictures $1998$ ) tells the story of a major legal battle that took place in the small town of Woburn, Massachusetts. A town well that supplied water to eastern Woburn residents was contaminated by industrial chemicals. During the period that residents drank water from this well, $16$ of the $414$ babies born had birth defects. On the west side of Woburn, $3$ of the $228$ babies born during the same time period had birth defects.

Explain why the conditions for using two-sample z procedures to perform inference about $p 1 - p 2$ are not met in the settings

Shrubs and ﬁre Fires are a serious threat to shrubs in dry climates. Some shrubs can resprout from their roots after their tops are destroyed. One study of resprouting took place in a dry area of Mexico. $7$ The investigators randomly assigned shrubs to treatment and control groups. They clipped the tops of all the shrubs. They then applied a propane torch to the stumps of the treatment group to simulate a ﬁre. All $12$ of the shrubs in the treatment group were resprouted. Only $8$ of the $12$ shrubs in the control group were resprouted.

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