Question 1

For which of the following combinations of sample size and population proportion would the standard deviation of   be smallest? ​

Accepted Answer

A) n = 40 and p = 0.3 
B) n = 60 and p = 0.4 
C) n = 100 and p = 0.5 
D) n = 200 and p = 0.6 
E) n = 300 and p = 0.7 
A) n = 40 and p = 0.3 
B) n = 60 and p = 0.4 
C) n = 100 and p = 0.5 
D) n = 200 and p = 0.6 
E) n = 300 and p = 0.7

Question 2

Which of the following statements is a population proportion? ​

Accepted Answer

A) A state census reports that 54% of the state's citizens owns at least one dog.. 
B) Out of 50 randomly-selected individuals, 19 indicated that they snore during sleep. 
C) The mean lifetime of all cell phone batteries is 11.3 hours. 
D) For a randomly-selected group of 20 computers running the Ubuntu operating system, the mean boot time was 28 seconds. 
E) None of these 
A) A state census reports that 54% of the state's citizens owns at least one dog.. 
B) Out of 50 randomly-selected individuals, 19 indicated that they snore during sleep. 
C) The mean lifetime of all cell phone batteries is 11.3 hours. 
D) For a randomly-selected group of 20 computers running the Ubuntu operating system, the mean boot time was 28 seconds. 
E) None of these

Question 3

For n sufficiently large, the distribution of   is approximately a standard normal distribution.

Accepted Answer

A) True 
 B)False

Question 4

As n grows larger, the mean of the sampling distribution of   gets closer to μ.

Accepted Answer

A) True 
 B)False

Question 5

What is a sampling distribution of a statistic?

Accepted Answer

The distribution of the possible values

Question 6

The distribution of   will always have the same shape as the distribution of the population being sampled.

Accepted Answer

A) True 
 B)False

Question 7

Consider the following "population": {2, 2, 4, 5}. Suppose that a random sample of size n = 2 is to be selected without replacement from this population. There are 6 possible samples (since the order of selection does not matter). Compute the sample mean for each of these samples and use that information to construct the sampling distribution of   . (Display it in table form.)

Accepted Answer

The 6 possible samples include

Question 8

The sampling distribution of   tends to be more spread out for larger sample sizes than for smaller sample sizes.

Accepted Answer

A) True 
 B)False

Question 9

A random sample is to be selected from a population that has a proportion of successes p = 0.50. Determine the mean and standard deviation of the sampling distribution of   for the sample size n = 100. ​

Accepted Answer

A) mean:   = 0.50; standard deviation:   = 0.05 
B) mean:   = 0.50; standard deviation:   = 0.075 
C) mean:   = 0.50; standard deviation:   = 0.041 
D) mean:   = 0.85; standard deviation:   = 0.48 
E) mean:   = 0.85; standard deviation:   = 0.048 
A) mean:   = 0.50; standard deviation:   = 0.05 
B) mean:   = 0.50; standard deviation:   = 0.075 
C) mean:   = 0.50; standard deviation:   = 0.041 
D) mean:   = 0.85; standard deviation:   = 0.48 
E) mean:   = 0.85; standard deviation:   = 0.048

Question 10

One method for estimating abundance of animals is known as line-intercept sampling. The theory of this method, when applied to Alaskan wolverines, predicts that p = 0.453 of attempts to locate wolverine tracks should be successful. Suppose that biologists will make 100 attempts to locate wolverine tracks in random locations in Alaska.
a)Show that this sample size is large enough to justify using the normal approximation to the sampling distribution of   .
b)What is the mean of the sampling distribution of   ?
c)What is the standard deviation of the sampling distribution of   ?
d)What is the probability that a sample proportion,   , would differ from p = 0.453 by as much as 0.05?

Accepted Answer

a)np = 100(.453) = 45.3 ≥ 10 a

Question 11

Some colleges now allow students to rent textbooks for a semester. Suppose that 73% of all students enrolled at a particular college would rent textbooks if that option were available to them. If the campus bookstore uses a random sample of size 40 to estimate the proportion of students at the college who would rent textbooks, then what is the standard deviation of the sampling distribution of   ? ​

Accepted Answer

A) 0.079 
B) 0.177 
C) 0.070 
D) 0.031 
E) 0.197 
A) 0.079 
B) 0.177 
C) 0.070 
D) 0.031 
E) 0.197

Question 12

Consider sampling from a skewed population. As the sample size, n, increases, some characteristics of the sampling distribution of   change. Does an increasing sample size cause changes in the characteristics of the sampling distribution shown below? If so, specifically how does the sampling distribution change?
a)The mean of the sampling distribution of   b)The standard deviation of the sampling distribution of   c)The shape of the sampling distribution of

Accepted Answer

a)As the sample size increases

Question 13

The closer p is to 0 or 1, the larger n must be in order for the distribution of   to be approximately normal.

Accepted Answer

A) True 
 B)False

Question 14

In a random sample of 79 students at a university, 7 had the flu. ​
Suppose you are interested in learning about the value of p, the proportion of all students at this university who have the flu. This proportion can be estimated using the sample proportion,   . What is the value of   for this sample?
​

Accepted Answer

A) 0.097 
B) 0.250 
C) 0.089 
D) 0.081 
E) 0.700 
A) 0.097 
B) 0.250 
C) 0.089 
D) 0.081 
E) 0.700

Question 15

The principal at Thomas Jefferson High School has been asked to estimate the proportion of students at KHS who drive to school and use the school parking lot. He takes a random sample of size n = 32 students and calculates a sample proportion,   = 0.8. "Now," he exclaims, "since my sample size is greater than 30, the sampling distribution of the sample proportion is approximately normal." Write a short paragraph that explains why his statement is not correct.

Accepted Answer

The Principal's statement is not accurat

For which of the following combinations of sample size and population proportion would the standard deviation of be smallest?

Which of the following statements is a population proportion?

For n sufficiently large, the distribution of is approximately a standard normal distribution.

As n grows larger, the mean of the sampling distribution of gets closer to μ.

What is a sampling distribution of a statistic?

The distribution of will always have the same shape as the distribution of the population being sampled.

The sampling distribution of tends to be more spread out for larger sample sizes than for smaller sample sizes.

A random sample is to be selected from a population that has a proportion of successes p = 0.50. Determine the mean and standard deviation of the sampling distribution of for the sample size n = 100.

The closer p is to 0 or 1, the larger n must be in order for the distribution of to be approximately normal.

In a random sample of 79 students at a university, 7 had the flu. Suppose you are interested in learning about the value of p, the proportion of all students at this university who have the flu. This proportion can be estimated using the sample proportion, . What is the value of for this sample?

Collecting Data in Reasonable Ways

Graphical Methods for Describing Data Distributions

Numerical Methods for Describing Data Distributions

Describing Bivariate Numerical Data

Probability

Random Variables and Probability Distributions

An Overview of Statistical Inference - Learning From Data

Estimating a Population Proportion

Asking and Answering Questions About a Population Proportion

Asking and Answering Questions About the Difference Between Two Proportions

Asking and Answering Questions About a Population Mean

Asking and Answering Questions About the Difference Between Two Means

Learning From Categorical Data

Understanding Relationships - Numerical Data Part 2

Asking and Answering Questions About More Than Two Means

Filters

Exam 8: Sampling Variability and Sampling Distributions

For which of the following combinations of sample size and population proportion would the standard deviation of be smallest? ​

Which of the following statements is a population proportion? ​

For n sufficiently large, the distribution of is approximately a standard normal distribution.

As n grows larger, the mean of the sampling distribution of gets closer to μ.

What is a sampling distribution of a statistic?

The distribution of will always have the same shape as the distribution of the population being sampled.

The sampling distribution of tends to be more spread out for larger sample sizes than for smaller sample sizes.

A random sample is to be selected from a population that has a proportion of successes p = 0.50. Determine the mean and standard deviation of the sampling distribution of for the sample size n = 100. ​

The closer p is to 0 or 1, the larger n must be in order for the distribution of to be approximately normal.

Collecting Data in Reasonable Ways

Graphical Methods for Describing Data Distributions

Numerical Methods for Describing Data Distributions

Describing Bivariate Numerical Data

Probability

Random Variables and Probability Distributions

An Overview of Statistical Inference - Learning From Data

Estimating a Population Proportion

Asking and Answering Questions About a Population Proportion

Asking and Answering Questions About the Difference Between Two Proportions

Asking and Answering Questions About a Population Mean

Asking and Answering Questions About the Difference Between Two Means

Learning From Categorical Data

Understanding Relationships - Numerical Data Part 2

Asking and Answering Questions About More Than Two Means

Filters

For which of the following combinations of sample size and population proportion would the standard deviation of be smallest?

Which of the following statements is a population proportion?

A random sample is to be selected from a population that has a proportion of successes p = 0.50. Determine the mean and standard deviation of the sampling distribution of for the sample size n = 100.