Chapter 7 AP Stat

At a particular college, 78% of all students are receiving some kind of financial aid. The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?

• 78% is a population and 72% is a sample.

• 72% is a population and 78% is a sample.

• 78% is a parameter and 72% is a statistic.

• 72% is a parameter and 78% is a statistic.

In a residential neighborhood, the median value of a house is $200,000. For which of the following sample sizes is the sample median most likely to be above $250,000?

• n=10

• n=50

• n=100

• n=1000

The magazine Sports Illustrated asked a random sample of 750 Division I college athletes, “Do you believe performance enhancing drugs are a problem in college sports?” Suppose that 30% of all Division I athletes think that these drugs are a problem. Let p ˆ be the sample proportion who say that these drugs are a problem.

Which of the following are the mean and standard deviation of the sampling distribution of the sample proportion p ˆ ?

• Mean = 0.30, SD = 0.017

• Mean = 0.30, SD = 0.55

• Mean = 0.30, SD = 0.0003

• Mean = 225, SD = 12.5

Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 515 and standard deviation 114. You choose an SRS of 100 students and average their SAT Math scores.Suppose that you do this many, many times. The mean of the average scores you get should be close to

• 515

• 515/100 = 5.15

• 15.5

• none of these

Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 515 and standard deviation 114. You choose an SRS of 100 students and average their SAT Math scores.Suppose that you do this many, many times. The standard deviation of the average scores you get should be close to

• 114

• 114/100 = 1.14

• 11.4

• none of these

Conditions for Means

• Random

• Central limit theorem: n ≥ 30

• 10% condition

• Independence of individual samples

Select the best answer. The magazine Sports Illustrated asked a random sample of 750 Division I college athletes, "Do you believe performance-enhancing drugs are a problem in college sports?" Suppose that 30% of all Division I athletes think that these drugs are a problem. Let phat

be the sample proportion who say that these drugs are a problem. The sampling distribution of

phat is approximately Normal because

• there are at least 7500 Division I college athletes

• np = 225 and n(1 - p) = 525 are both at least 10

• a random sample was chosen

• the athletes' responses are quantitative

A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of health of such children in later years examined a random sample of 219 children. Their mean weight at birth was x = 810 grams. This sample mean is an unbiased estimator of the mean weight  in the population of all ELBW babies, which means that

• in all possible samples of size 219 from this population, the mean of the values of x will equal 810.

• in all possible samples of size 219 from this population, the mean of the values of x will equal mew.

• as we take larger and larger samples from this population, x will get closer and closer to mew.

• in all possible samples of size 219 from this population, the values of x will have a distribution that is close to Normal.

The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that

• as we look at more and more bulbs, their average burnout time gets ever closer to the mean mew for all bulbs of this type.

• the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution.

• the average burnout time of a large number of bulbs has a sampling distribution with similar shape but not as extreme (skewed, but not as strongly) as the population distribution

• the average burnout time for a large number of bulbs has a sampling distribution that is exactly Normal

• the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

Suppose you take a random sample of size 25 from a population with mean of 120 and a standard deviation of 15. Your sample has a mean of 115 and a standard deviation of 13.8. Which of the following has a mean of 120 and a standard deviation of 3?

• the distribution of the population

• the distribution of the sample data

• the sampling distribution of the sample mean

• the sampling distribution of the population mean

• No important distribution related to this situation has the given mean and standard deviation.