AP Stats Quiz Unit 5

Which of the following conditions will create a biased estimator of a population parameter?

D, The expected value of the estimator is not equal to the population parameter.

The statistic x¯ is used as an estimator for which of the following?

D, μ

A certain statistic dˆ is being used to estimate a population parameter D. The expected value of dˆ is not equal to D. What property does dˆ exhibit?

E, dˆ is biased.

The following graphs show the sampling distributions for two different point estimators, R and W, of the same population parameter. Which of the following statements is true?

A, both R and W are unbiased

At a large corporation, the distribution of years of employment for the employees has mean 20.6 years and standard deviation 5.3 years. A random sample of 100 employees was selected and surveyed about employee satisfaction. The sample of employees had a mean 20.3 years and standard deviation 6.1 years. Remy claims that the mean of the sampling distribution of the sample mean for samples of size 100 is 20.6 years. Is Remy's claim correct?

E, Yes. The mean of the sampling distribution is 20.6 years.

A fair die has its faces numbered from 1 to 6. Let random variable F represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3.5 and standard deviation 1.7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded. The mean and standard deviation of the results of the simulation should be close to which of the following?

ddd

A sample of size n will be selected from a population with population proportion p. Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal?

A, Both np and n(1−p) are at least 10.

The distribution of prices for a certain car model is approximately normal with mean $21,800 and standard deviation $400. A random sample of 4 cars of the model will be selected. What is the correct unit of measure for the mean of the sampling distribution of x¯ ?

A, Dollars

For a certain population of sea turtles, 18 percent are longer than 6.5 feet. A random sample of 90 sea turtles will be selected. What is the standard deviation of the sampling distribution of the sample proportion of sea turtles longer than 6.5 feet for samples of size 90 ?

B, 0.18(1−0.18)90−−−−−−−−√

The mean number of pets owned by the population of students at a large high school is 3.2 pets per student with a standard deviation of 1.7 pets. A random sample of 16 students will be selected and the mean number of pets for the sample will be calculated. What is the mean of the sampling distribution of the sample mean for samples of size 16 ?

B, 3.2

At a large corporation, 6,000 employees from department A and 4,000 employees from department B are attending a training session. A random sample of 500 employees attending the session will be selected. Consider two sampling methods: with replacement and without replacement. How will the methods affect the standard deviations of the sampling distribution of the sample proportion of employees from department B?

B, Sampling without replacement will result in a standard deviation less than but close to 0.4(0.6)500−−−−−√.

A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation. Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?

B, The sample size was not sufficiently large.

For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?

C, A random sample of 10 taken from a population distribution that is skewed to the right

A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured?

C, Approximately normal

On any given day, the proportion of workers at a factory who are more than 5 minutes late to work is 0.11. A random sample of 20 workers will be selected. Which of the following is the best interpretation of the mean of the sampling distribution of the sample proportion of workers in the sample who are more than 5 minutes late to work for samples of size 20 ?

C, For a random sample of 20 workers, the proportion of workers who are more than 20 minutes late to work will be 0.11.

For which of the following is the shape of the sampling distribution of the sample mean approximately normal? A random sample of size 5 from a population that is approximately normal A random sample of size 10 from a population that is strongly skewed to the right A random sample of size 60 from a population that is strongly skewed to the left

C, I and II only

A reading specialist wanted to estimate the mean word length, in number of letters, for an elementary school history textbook. The specialist took repeated random samples of size 100 words and estimated the mean and standard deviation of the sampling distribution to be 4.9 letters and 0.15 letter, respectively. Based on the estimates for the sampling distribution, which of the following provides the best estimates of the population parameters?

C, Mean 4.9 letters and standard deviation 1.5 letters

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

C, The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

A bag contains chips of which 27.5 percent are blue. A random sample of 5 chips will be selected one at a time and with replacement. What are the mean and standard deviation of the sampling distribution of the sample proportion of blue chips for samples of size 5 ?

C, The mean is 0.275, and the standard deviation is 0.275(0.725)5−−−−−−−−√.

A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion of those who make a donation when contacted by phone is known to be p=0.05. For samples of size 100, which of the following best interprets the mean of the sampling distribution of the sample proportion of people who make a donation when contacted by phone?

C, The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

City officials estimate that 46 percent of all city residents are in favor of building a new city park. A random sample of 150 city residents will be selected. Suppose that 51 percent of the sample are in favor of building a new city park. Which of the following is true about the sampling distribution of the sample proportion for samples of size 150 ?

D, The distribution is approximately normal, and the mean is 0.46.

A recent report indicated that 90 percent of adults in a certain region actively try to include vegetables in their diet. A simulation was conducted that consisted of 50 trials with a population parameter of 0.9. Each trial consisted of a sample size of 10. The number of successes out of 10 was recorded, where success represented an adult trying to include vegetables in the diet. Five possible simulation results are shown. Which simulation is the best match to the one described?

E

A manufacturer of cell phone screens has found that 5 percent of all screens produced have defects. Let pd represent the population proportion of all cell phone screens with a screen defect, therefore pd=0.05. For the sampling distribution of the sample proportion of cell phone screens from this manufacturer with a screen defect for sample size 400, μpˆd=0.05. Which of the following is the best interpretation of μpˆd=0.05 ?

E, For all samples of size 400 from this population, the standard deviation of all resulting sample proportions of cell phone screens with a screen defect is 0.05.

At a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. A random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. For samples of size 5, which of the following is the best interpretation of P(x¯>22)≈0.05?

E, For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.

Samples G and H were selected from the same population of quantitative data and the mean of each sample was determined. The mean of sample G is equal to the mean of the population. Which of the following statements must be true? The mean of sample H must also be equal to the population mean. The mean of sample G, x¯G, is a point estimator for the mean of the population. The mean of sample H, x¯H, is a point estimator for the mean of the population.

E, II and III

The distribution of age for players of a certain professional sport is strongly skewed to the right with mean 26.8 years and standard deviation 4.2 years. Consider a random sample of 4 players and a different random sample of 50 players from the population. Which of the following statements is true about the sampling distributions of the sample mean ages for samples of size 4 and samples of size 50 ?

E, Only the sampling distribution for size 50 will be approximately normal, and the mean for both will be 26.8.

A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.

E, The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.