Question 1

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

Accepted Answer

E

Question 2

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

True

Question 3

What is a sampling distribution of a statistic?

Accepted Answer

The distribution of the possible values of a statistic is called its sampling distribution.
Note: Generally if the student communicates the idea that the sampling distribution associates different values of the statistic with their probabilities, he or she should get credit.

Question 4

The principal at John F. Kennedy High School has been asked to provide the average number of classes taken by the students at KHS. Since the computer system is down, she takes her alphabetized list of students, randomly selects 50 students, determines the number of classes each of the 50 selected students is taking, and calculates  = 5.4. She then reports to the PTA "Since I took a large random sample, the population mean number of classes taken by the students at KHS is 5.4." Write a short paragraph to send to her that explains why her statement is not correct.

Accepted Answer

The answer of The principal at John F. Kennedy High...

Question 5

Suppose that a particular candidate for public office is favored by 43% of all registered voters in the district A polling organization will take a random sample of 50 of these voters and will use  , the sample proportion, to estimate p. ​
Determine the standard deviation of  .
​
A)0.005
B)0.035
C)0.100
D)0.043
E)0.070

Accepted Answer

The answer of Suppose that a particular candidate for public...

Question 6

Which of the following statements is a population proportion? ​
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

Accepted Answer

A population proportion refers to the percentage of a certain characteristic within an entire population. Choice A, stating that 54% of the state's citizens own at least one dog, is a population proportion because it describes a characteristic (dog ownership) of the entire population of the state.

Question 7

A sampling distribution of  can be regarded as approximately normal when what conditions are met? ​
A)n ≥ 30
B)n ≥ 10
C)np ≥ 5 and n(1 - p) ≥ 5
D)n ≥ 5
E)np ≥ 10 and n(1 - p) ≥ 10

Accepted Answer

The answer of A sampling distribution of  can be...

Question 8

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

Accepted Answer

The answer of The distribution of  will always have...

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. ​
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

Accepted Answer

The answer of A random sample is to be selected...

Question 10

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

Accepted Answer

The answer of In a random sample of 79 students...

Question 11

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

Accepted Answer

The answer of For n sufficiently large, the distribution of...

Question 12

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

Accepted Answer

The answer of The sampling distribution of  tends to...

Question 13

If p = 0.90, a sample size of n = 10 is large enough for the sampling distribution to be well approximated by a normal distribution.

Accepted Answer

The rule of thumb for the normal approximation to be appropriate is that both np and n(1-p) should be greater than or equal to 10. In this case, np = 9 and n(1-p) = 1, which does not meet the criteria.

Question 14

The standard deviation of the distribution of  decreases as n increases.

Accepted Answer

The answer of The standard deviation of the distribution of...

Question 15

The mean of the sampling distribution of  is p no matter how large n is.

Accepted Answer

The answer of The mean of the sampling distribution of...

Question 16

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

Accepted Answer

The answer of Some colleges now allow students to rent...

Question 17

A statistic is a characteristic of the population.

Accepted Answer

A statistic is actually a characteristic of a sample, not the population as a whole. A parameter is a characteristic of the population.

Question 18

Suppose that 8% of the customers of a cable television company watch the Jewelry Network channel at least once a week. The cable company does not know the actual proportion of all customers who watch the channel at least once a week and is trying to decide whether to replace this channel with a new local station. The company plans to take a random sample of 150 customers and to use  as an estimate of the population proportion. ​
Determine the standard deviation of  .
​
A)0.022
B)0.006
C)2.400
D)0.070
E)0.041

Accepted Answer

The answer of Suppose that 8% of the customers of...

Question 19

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

Accepted Answer

The answer of As n grows larger, the mean of...

Question 20

Which of the following symbols is used to indicate a population proportion? ​
A)p
B) 
C)μ
D)σ
E)

Accepted Answer

The answer of Which of the following symbols is used...

Quiz 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?

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

What is a sampling distribution of a statistic?

Suppose that a particular candidate for public office is favored by 43% of all registered voters in the district A polling organization will take a random sample of 50 of these voters and will use , the sample proportion, to estimate p. Determine the standard deviation of .

Which of the following statements is a population proportion?

A sampling distribution of can be regarded as approximately normal when what conditions are met?

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

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.

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?

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

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

If p = 0.90, a sample size of n = 10 is large enough for the sampling distribution to be well approximated by a normal distribution.

The standard deviation of the distribution of decreases as n increases.

The mean of the sampling distribution of is p no matter how large n is.

A statistic is a characteristic of the population.

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

Which of the following symbols is used to indicate a population proportion?

Quiz 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? ​

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

What is a sampling distribution of a statistic?

Suppose that a particular candidate for public office is favored by 43% of all registered voters in the district A polling organization will take a random sample of 50 of these voters and will use , the sample proportion, to estimate p. ​ Determine the standard deviation of . ​

Which of the following statements is a population proportion? ​

A sampling distribution of can be regarded as approximately normal when what conditions are met? ​

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

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. ​

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

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

If p = 0.90, a sample size of n = 10 is large enough for the sampling distribution to be well approximated by a normal distribution.

The standard deviation of the distribution of decreases as n increases.

The mean of the sampling distribution of is p no matter how large n is.

A statistic is a characteristic of the population.

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

Which of the following symbols is used to indicate a population proportion? ​

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

Suppose that a particular candidate for public office is favored by 43% of all registered voters in the district A polling organization will take a random sample of 50 of these voters and will use , the sample proportion, to estimate p. Determine the standard deviation of .

Which of the following statements is a population proportion?

A sampling distribution of can be regarded as approximately normal when what conditions are met?

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.

Which of the following symbols is used to indicate a population proportion?