Question 1

The desired situation is when the sampled population is _____ the targeted population.
A) identical to
B) larger than
C) smaller than
D) more varied than

Accepted Answer

The goal of sampling is to obtain a representative sample of the targeted population. If the sampled population is identical to the targeted population, this means that the sample is a true representation of the population, and the results obtained from the sample can be generalized to the population as a whole. If the sampled population is larger or smaller than the targeted population or more varied than the targeted population, the results obtained from the sample may not be applicable or may be biased. Therefore, the best choice is A) identical to.

Question 2

The standard error of the proportion will become larger as​
A) ​n increases.
B) ​p approaches 0.
C) ​p approaches .5.
D) ​p approaches 1.

Accepted Answer

The standard error of the proportion is largest when p = 0.5 because the formula for the standard error of a proportion is sqrt[p(1-p)/n], and the product p(1-p) reaches its maximum value when p = 0.5.

Question 3

The expected value of equals the mean of the population from which the sample is drawn​
A) ​only if the sample size is 30 or greater.
B) ​only if the sample size is 50 or greater.
C) ​only if the sample size is 100 or greater.
D) ​for any sample size.

Accepted Answer

The expected value of a sample is equal to the population mean regardless of the sample size. This is a fundamental concept in statistics.

Question 4

The value of the _____ is used to estimate the value of the population parameter
A) population statistic
B) sample parameter
C) population estimate
D) sample statistic

Accepted Answer

The sample statistic is used to estimate the population parameter. Sample statistics are calculated from a sample of data and provide information about the characteristics of that sample, such as its mean or standard deviation. Population parameters, on the other hand, are characteristics of the entire population that we are interested in estimating, such as the population mean or standard deviation. By using sample statistics to estimate population parameters, we can make inferences about the population as a whole based on the information we have from the sample.

Question 5

A probability sampling method in which we randomly select one of the first k elements and then select every k^th element thereafter is _____ sampling. A) stratified random B) cluster C) systematic D) convenience

Accepted Answer

The described sampling method is systematic sampling, as it involves selecting every kth element from a larger population. Stratified random sampling involves dividing a population into subgroups and randomly selecting from each subgroup, cluster sampling involves randomly selecting groups/clusters of individuals to sample, and convenience sampling involves selecting individuals who are conveniently available or easily accessible. None of these methods match the described sampling approach.

Question 6

The extent of the sampling error might be affected by all of the following factors except the
A) variability of the population.
B) expected value of the sample statistic
C) sample size.
D) sampling method used.

Accepted Answer

The expected value of the sample statistic does not affect the extent of the sampling error. The other factors listed (variability of the population, sample size, and sampling method used) can all impact the extent of sampling error.

Question 7

The population being studied is usually considered _____ if it involves an ongoing process that makes listing or counting every element in the population impossible.
A) finite
B) infinite
C) skewed
D) symmetric

Accepted Answer

An ongoing process that makes listing or counting every element in the population impossible would indicate an infinite population.

Question 8

The standard deviation of  is referred to as the _____ proportion.
A) standard
B) sample mean
C) deviated
D) standard error of the

Accepted Answer

The standard deviation of a sample is used to estimate the standard error of the mean for that sample. Therefore, the standard deviation of 11eb12c9_c6a5_99e8_b394_a76429bd431e_TB6985_11 would be referred to as the standard error of the sample mean.

Question 9

In a local university, 70% of the students live in the dormitories. A random sample of 75 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is between 0.69 and 0.72 is
A) 0.7778.
B) 0.2222.
C) 0.2347.
D) 0.7653.

Accepted Answer

The answer of In a local university, 70% of the...

Question 10

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size _____ of being selected.
A) N has the same probability
B) n has a probability of 0.5
C) n has a probability of 0.1
D) n has the same probability

Accepted Answer

In a simple random sample of size n from a finite population of size N, each possible sample of size n has the same probability of being selected. This ensures that every element of the population has an equal chance of being included in the sample.

Question 11

In a local university, 70% of the students live in the dormitories. A random sample of 75 students is selected for a particular study. The standard deviation of  , known as the standard error of the proportion is approximately
A) 0.5292.
B) 5.2915.
C) 0.0529.
D) 52.915.

Accepted Answer

The formula for the standard error of proportion is SEp = sqrt(p(1-p)/n), where p is the proportion of interest (0.7 in this case) and n is the sample size (75 in this case). Plugging in the numbers, we get SEp = sqrt(0.7(1-0.7)/75) which simplifies to approximately 0.0529. Therefore, the answer is C.

Question 12

All of the following are true about the standard error of the mean except​
A) ​it is larger than the standard deviation of the population.
B) ​it decreases as the sample size increases.
C) ​its value is influenced by the standard deviation of the population.
D) ​it measures the variability in sample means.

Accepted Answer

The standard error of the mean is actually smaller than the standard deviation of the population.

Question 13

It is impossible to construct a frame for a(n) _____ population.
A) finite
B) infinite
C) target
D) defined

Accepted Answer

It is impossible to construct a frame for an infinite population because the population is limitless, making it impossible to accurately capture and identify every individual or unit within the population.

Question 14

Which of the following statements about cluster sampling is false?​
A) ​All elements within the randomly selected clusters form the sample
B) ​It generally requires a smaller total sample size than simple random sampling
C) ​Ideally, each cluster is a representative small-scale version of the entire population
D) ​It provides the best results when the elements within the clusters are not alike

Accepted Answer

Cluster sampling generally requires a larger total sample size than simple random sampling to achieve the same level of precision because of the potential for increased variability within clusters.

Question 15

When the population has a normal distribution, the sampling distribution of  is normally distributed for any sample
A) size.
B) size of 30 or more.
C) size of 50 or more.
D) from a finite population.

Accepted Answer

The answer of When the population has a normal distribution,...

Question 16

In stratified random sampling,​
A) ​randomly selected elements within each of the strata form the sample.
B) ​all elements within the randomly selected strata form the sample.
C) ​randomly selected elements within the randomly selected strata form the sample.
D) ​all elements within each of the strata form the sample.

Accepted Answer

In stratified random sampling, the population is divided into homogeneous subgroups called strata. Then a random sample is selected from each stratum. The best choice is A, as it involves randomly selecting elements within each of the strata to form the final sample. This ensures that the sample is representative of the entire population and reduces the sampling error.

Question 17

The standard deviation of  is referred to as the​
A) ​standard mean of x.
B) ​standard error of the mean.
C) ​sample standard mean.
D) ​sample mean deviation.

Accepted Answer

The answer of The standard deviation of  is referred...

Question 18

In a local university, 70% of the students live in the dormitories. A random sample of 75 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.60 is
A) 0.0294.
B) 0.9706.
C) 0.0228.
D) 0.9772.

Accepted Answer

The sample proportion of students living in dormitories follows a normal distribution (by the Central Limit Theorem) with mean $p = 0.70$ and standard error $SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.70(0.30)}{75}}$. To find the probability that the sample proportion is at least 0.60, we calculate the Z-score for 0.60: $Z = \frac{0.60 - 0.70}{SE}$, and then find the probability to the right of this Z-score in the standard normal distribution. This calculation gives a high probability, indicating that it is very likely to observe a sample proportion of at least 0.60 when the true proportion is 0.70, hence option B is correct.

Question 19

A random sample of 144 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.3 ounces. In this problem the 0.3 is
A) a parameter.
B) a statistic.
C) the standard error of the mean.
D) the average content of colognes in the long run.

Accepted Answer

In this problem, 0.3 ounces is the standard deviation of the population, which is a fixed characteristic of the population and is therefore a parameter, not a statistic or the standard error of the mean. It is also not the average content of colognes in the long run, as that would require multiple samples and averaging their results.

Question 20

The population we want to make inferences about is th​e
A) ​sampled population.
B) ​frame.
C) ​target population.
D) ​finite population.

Accepted Answer

The target population is the population about which we want to make inferences. It is the larger group to which we wish to generalize our findings.

Quiz 7: Sampling and Sampling Distributions

The desired situation is when the sampled population is _____ the targeted population.

The standard error of the proportion will become larger as

The expected value of equals the mean of the population from which the sample is drawn

The value of the _____ is used to estimate the value of the population parameter

A probability sampling method in which we randomly select one of the first k elements and then select every k^th element thereafter is _____ sampling.

The extent of the sampling error might be affected by all of the following factors except the

The population being studied is usually considered _____ if it involves an ongoing process that makes listing or counting every element in the population impossible.

The standard deviation of is referred to as the _____ proportion.

In a local university, 70% of the students live in the dormitories. A random sample of 75 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is between 0.69 and 0.72 is

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size _____ of being selected.

In a local university, 70% of the students live in the dormitories. A random sample of 75 students is selected for a particular study. The standard deviation of , known as the standard error of the proportion is approximately

All of the following are true about the standard error of the mean except

It is impossible to construct a frame for a(n) _____ population.

Which of the following statements about cluster sampling is false?

When the population has a normal distribution, the sampling distribution of is normally distributed for any sample

In stratified random sampling,

The standard deviation of is referred to as the

In a local university, 70% of the students live in the dormitories. A random sample of 75 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.60 is

A random sample of 144 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.3 ounces. In this problem the 0.3 is

The population we want to make inferences about is the