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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

Heavy bread? The mean weight of loaves of bread produced at the bakery where you work is supposed to be $1$ pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are producing loaves that are too light. Suppose you weigh an SRS of bread loaves and find that the mean weight is $0.975$ pound.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Explain why there is some evidence for the alternative hypothesis.

c. The P-value for the test in part (a) is $0.0806$ . Interpret the P-value.

d. What conclusion would you make at the $α = 0.01$ significance level?

Packaging DVDs $(6.2, 5.3)$ A manufacturer of digital video discs (DVDs) wants to be sure that the DVDs will fit inside the plastic cases used as packaging. Both the cases and the DVDs are circular. According to the supplier, the diameters of the plastic cases vary Normally with mean $μ = 5.3$ inches and standard deviation $σ = 0.01$ inch. The DVD manufacturer produces DVDs with mean diameter $μ = 5.26$ inches. Their diameters follow a Normal distribution with $σ = 0.02$ inch.

a. Let X = the diameter of a randomly selected case and Y = the diameter of a randomly selected DVD. Describe the shape, center, and variability of the distribution of the random variable X−Y. What is the importance of this random variable to the DVD manufacturer?

b. Calculate the probability that a randomly selected DVD will fit inside a randomly selected case.

c. The production process runs in batches of 100 DVDs. If each of these DVDs is paired with a randomly chosen plastic case, find the probability that all the DVDs fit in their cases.

Awful accidents Slow response times by paramedics, firefighters, and policemen can have serious consequences for accident victims. In the case of life-threatening injuries, victims generally need medical attention within $8$ minutes of the accident. Several cities have begun to monitor emergency response times. In one such city, emergency personnel took more than $8$ minutes to arrive on $22 %$ of all calls involving life-threatening injuries last year. The city manager shares this information and encourages these first responders to “do better.” After $6$ months, the city manager selects an SRS of 400 calls involving life- threatening injuries and examines the response times. She then performs a test at the $α = 0.05$ level of $H_{0}$ : $p = 0.22$ versus $H_{a} : p < 0.22$ , where $p$ is the true proportion of calls involving life-threatening injuries during this $6$ -month period for which emergency personnel took more than $8$ minutes to arrive.

a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the manager’s choice of $α = 0.05$ ? Why or why not?

Opening a restaurant You are thinking about opening a restaurant and are

searching for a good location. From research you have done, you know that the mean income of those living near the restaurant must be over $\(85, 000$ to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of $50$ people living near one potential location. Based on the mean income of this sample, you will perform a test of

$H_{0} : μ = \) 85, 000$

$H_{a} : μ > $ 85, 000$

where $μ$ is the true mean income in the population of people who live near the restaurant. Describe a Type $I$ error and a Type $I I$ error in this setting, and give a possible consequence of each.

Teens and sex The Gallup Youth Survey asked a random sample of U.S. teens aged 13 to 17 whether they thought that young people should wait until marriage to have sex.14 The Minitab output shows the results of a significance test and a 95% confidence interval based on the survey data.

a. Define the parameter of interest.

b. Check that the conditions for performing the significance test are met in this case.

c. Interpret the P-value.

d. Do these data give convincing evidence that the actual population proportion differs from $0.5$ ? Justify your answer with appropriate evidence.

See all solutions

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