AP Statistics Unit 6 MCQ Quiz

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of those homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

• Approximately normal with mean $206,274 and standard deviation $3,788

• Approximately normal with mean $206,274 and standard deviation $37,881

• Approximately normal with mean $206,274 and standard deviation $520

• Strongly right-skewed with mean $206,274 and standard deviation $3,788

• Strongly right-skewed with mean $206,274 and standard deviation $37,881

Every Thursday, Matt and Dave’s Video Venture has “roll-the-dice” day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and a two are rolled, a second movie may be rented for $0.22. The average price paid for a second movie on roll-the-dice day is $0.47 with a standard deviation of $0.15. If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total amount paid for these second movies will exceed $15.00?

• 0

• 0.09

• 0.14

• 0.86

• 0.91

There are 120 students taking statistics at Francis Howell North High School. Assume that it is known that these students sleep for an average of 6.7 hours per night with a standard deviation of 2 hours.

Their teacher conducts a poll that asks 20 randomly selected students how many hours of sleep they got last night. Can we estimate the standard deviation of the sampling distribution of sample means by using

σx̄ = σ/√n = 2/√20 = 0.447 hours?

• No, because “hours of sleep” is not a continuous random variable

• No, because the sample is not less than 10% of the population

• No, because the Central Limit Theorem applies in this situation

• No, because we don’t know if the distribution of sleep hours is approximately normal

• Yes, because all of the conditions for using this formula have been met

In 2018, it was estimated that there were roughly 554,000 homeless people in the United States. The average shelter stay for homeless families with kids is 435 days. Assume a skewed left distribution with a standard deviation of 85 days. Consider random samples of size 100 taken from the distribution with the mean length of stay, x̄, recorded for each sample. Which of the following is the best description of the sampling distribution of x̄?

• Skewed left with mean 435 days and standard deviation 0.85 days

• Skewed left with mean 435 days and standard deviation 8.5 days

• Skewed left with mean 435 days and standard deviation 85 days

• Approximately normal with mean 435 days and standard deviation 0.85 days

• Approximately normal with mean 435 days and standard deviation 8.5 days

Random samples of size n are drawn from a population. The mean of each sample is calculated, and the standard deviation of this set of sample means is found. Then the procedure is repeated, this time with samples of size 4n. How does the standard deviation of the second group compare with the standard deviation of the first group?

• It will be the same.

• It will be twice as large.

• It will be four times as large.

• It will be half as large.

• It will be one-quarter as large.

The mean and standard deviation of the population {1, 5, 8, 11, 15} are μ = 8 and σ = 4.8, respectively. Let S be the set of the 125 ordered triples (repeats allowed) of elements of the original population. Which of the following is a correct statement about the mean μx̄ and standard deviation σx̄ of the means of the triples in S?

• μx̄ = 8, σx̄ = 4.8

• μx̄ = 8, σx̄ < 4.8

• μx̄ = 8, σx̄ > 4.8

• μx̄ < 8, σx̄ = 4.8

• μx̄ > 8, σx̄ > 4.8

The random variable describing the number of minutes high school students spend in front of a computer daily has a mean of 200 minutes. Samples of two different sizes result in sampling distributions with the two graphs below. Which of the following is a true statement?

• Based on these graphs, no comparison between the two sample sizes is possible.

• More generally, sample sizes have no effect on sampling distributions.

• The sample size in A is the same as the sample size in B.

• The sample size in A is less than the sample size in B.

• The sample size in A is greater than the sample size in B.

Which of the following is the central limit theorem?

• No matter how the population is distributed, as the sample size increases, the mean of the sample means becomes closer to the mean of the population.

• No matter how the population is distributed, as the sample size increases, the standard deviation of the sample means becomes closer to the standard deviation of the population divided by the square root of the sample size.

• If the population is normally distributed, then as the sample size increases, the sampling distribution of the sample mean becomes closer to a normal distribution.

• No matter how the original population is distributed, as the sample size increases, the sampling distribution of the sample mean becomes closer to a normal distribution.

• No matter how the original population is distributed, as the sample size increases, the distribution of the sample becomes closer to the distribution of the population.

What is a sampling distribution?

• A distribution of all the statistics that can be found in a given sample

• A histogram, or other such visual representation, showing the distribution of a sample

• A normal distribution of some statistic

• A distribution of all the values taken by a statistic from all possible samples of a given size

• All of the above

You take a simple random sample of size n = 25 from a very large population in which the true proportion is p = 0.1. Which statement below best describes what you know about the sampling distribution of p̂?

• μp̂ = 0.1; cannot calculate σp̂ ; the sampling distribution of p̂ is approximately normal

• μp̂ = 0.1; cannot calculate σp̂ ; the sampling distribution of p̂ is not approximately normal

• μp̂ = 0.1; σp̂ = 0.06; the sampling distribution of p̂ is roughly symmetric

• μp̂ = 0.1; σp̂ = 0.06; the sampling distribution of p̂ is skewed to the left

• μp̂ = 0.1; σp̂ = 0.06; the sampling distribution of p̂ is skewed to the right