Unit 6 Stats MC proportional intervals

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Inheritance

A Gallup Poll found that only 28% of American adults expect to inherit money or valuable possessions from a relative. The poll’s margin of error was ±3 percentage points at a 95% confidence level.

This means that

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1

Inheritance

A Gallup Poll found that only 28% of American adults expect to inherit money or valuable possessions from a relative. The poll’s margin of error was ±3 percentage points at a 95% confidence level.

This means that

The poll used a method that gets an answer within 3% of the truth about the population about 95% of the time.

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2

Genetics

Most people can roll their tongues, but many can’t. 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 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to

0.04

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3

Minimum sample size

You want to design a study to estimate the proportion of students at your school who agree with the statement, “The student government is an effective organization for expressing the needs of students to the administration.” You will use a 95% confidence interval, and you would like the margin of error to be 0.05 or less. The minimum sample size required is

385

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4

Increase in confidence

A 95% confidence interval for the mean reading achievement score for a population of third-grade students is (44.2, 54.2). Suppose you compute a 99% confidence interval using the same data. Which of the following statements is correct?

The 99% interval is wider

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5

Loans for college

A survey of 1025 randomly selected teens found that 20% of students aged 14 to 18 plan to borrow no money to pay for college. What's the margin of error for a 90% confidence interval for the proportion of all students aged 14 to 18 who plan to borrow no money to pay for college?

+-2.06%

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6

Religion

In describing the findings of a 2010 Public Religion Research Institute poll, researchers reported a 3% margin of error at a 95% confidence level. If they had used a 99% confidence level instead, their margin of error would have been:

More than 3%, because they reported greater confidence

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7

Standard error

In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately

0.0306

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8

Interpret confidence level

The report of a sample survey of 1,014 adults says, "With 95% confidence, between 9% and 15% of all Americans expect to spend more money on gifts this year than last year." The phrase "95% confidence" means

The method used to get the interval from 9% to 15%, when used over and over, produces intervals which include the true population percentage about 95% of the time.

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9

You want to calculate an 82% confidence interval for a population proportion from a random sample of size 100. What is the appropriate critical value?

1.34

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10

A local newspaper in a large city wants to assess support for the construction of a highway by-pass around the central business district to reduce downtown traffic. They survey a random sample of 1152 residents and find that 543 of them support the bypass. Which of the following is a 95% confidence interval for the proportion of residents who support construction of the bypass?

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