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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 9: Q 106. (page 611)

The most important condition for making an inference about a population mean from a significance test is that
a. the data come from a random sample.
b. the population distribution is exactly Normal.
c. the data contain no outliers.
d. the sample size is less than $10 %$ of the population size.
e. the sample size is at least $30$

Short Answer

Expert verified

The correct option is (a) the data come from a random sample.

Step by step solution

01

Given information

The information is drawn from a random sample.
The distribution of the population is perfectly Normal.
There are no outliers in the data.
The sample size is less than $10 %$ of the total population.
There are at least $30$ people in the sample.

02

Explanation

The most appropriate response to the given statement is “The information comes from a well-designed randomized sample or experiment.”

So the correct option is (a).

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Most popular questions from this chapter

Explaining confidence: Here is an explanation from a newspaper concerning one of its opinion polls. Explain what is wrong with the following statement.

For a poll of $1600$ adults, the variation due to sampling error is no more than $3$

percentage points either way. The error margin is said to be valid at the $95 %$

confidence level. This means that, if the same questions were repeated in $20$ polls, the results of at least $19$ surveys would be within $3$ percentage points of the results of this survey.

Walking to school A recent report claimed that $13 %$ of students typically walk to school. DeAnna thinks that the proportion is higher than $0.13$ at her large elementary school. She surveys a random sample of $100$ students and finds that $17$ typically walk to school. DeAnna would like to carry out a test at the $α = 0.05$ significance level of $H_{0} : p = 0.13$ versus $H_{a} : p > 0.13$ , where $p$ = the true proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.

Members of the city council want to know if a majority of city residents supports a $1 %$ increase in the sales tax to fund road repairs. To investigate, they survey a random sample of $300$ city residents and use the results to test the following hypotheses:

$H_{0} : p = 0.50$

$H_{a} : p > 0.50$

where $p$ is the proportion of all city residents who support a 1% increase in the sales tax to fund road repairs.

A Type I error in the context of this study occurs if the city council

a. finds convincing evidence that a majority of residents supports the tax increase, when in reality there isn’t convincing evidence that a majority supports the increase.

b. finds convincing evidence that a majority of residents supports the tax increase, when in reality at most $50 %$ of city residents support the increase.

c. finds convincing evidence that a majority of residents supports the tax increase, when in reality more than $50 %$ of city residents do support the increase.

d. does not find convincing evidence that a majority of residents supports the tax increase, when in reality more than $50 %$ of city residents do support the increase.

Potato power problems Refer to Exercises $85$ and $87$

a. Explain one disadvantage of using $α = 0.10$ instead of $α = 0.05$ when

performing the test.

b. Explain one disadvantage of taking a random sample of $500$ potatoes instead of $250$ potatoes from the shipment.

Bullies in middle school A media report claims that more than $75 %$ of

middle school students engage in bullying behavior. A University of Illinois study on aggressive behavior surveyed a random sample of $558$ middle school students. When asked to describe their behavior in the last $30$ days, $445$ students admitted that they had engaged in physical aggression, social ridicule, teasing, name-calling, and issuing threats —all of which would be classified as bullying. Do these data provide convincing evidence at the $α = 0.05$ significance level that the media report’s claim is correct?

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