Question 1

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

Accepted Answer

When the population is normally distributed, the sampling distribution of the sample mean $ \bar x $ is normally distributed for any sample size due to the properties of the normal distribution.

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

A frame is a list of all the units in the population from which a sample is drawn. An infinite population cannot be listed or exhaustively characterized, making it impossible to construct a frame.

Question 4

In a local university, 40% of the students live in the dormitories.A random sample of 80 students is selected for a particular study.The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is
A) 0.4664
B) 0.9328
C) 0.0336
D) 0.0672

Accepted Answer

We can use the Central Limit Theorem to approximate the proportion distribution as normal distribution with mean = 0.4 and variance = (0.4)(0.6)/80 = 0.00225. Then, we can standardize and calculate the z-scores for the given range:

z1 = (0.30 - 0.4)/sqrt(0.00225) = -4.71
z2 = (0.50 - 0.4)/sqrt(0.00225) = 4.71

Using a standard normal table or a calculator, we can find the area between these two z-scores:

P(-4.71 < Z < 4.71) = 0.9328

Therefore, the probability that the sample proportion is between 0.30 and 0.50 is 0.9328 or choice B.

Question 5

The standard deviation of $ \bar x $ 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 standard deviation of the sample mean is called the standard error of the mean.

Question 6

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 a population impossible suggests an infinite population, in which case the population is not restricted to any particular size.

Question 7

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

The answer of Which of the following statements about cluster...

Question 8

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 9

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, as it is a measure of the variability among sample means, not individual observations within a sample.

Question 10

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 first divided into homogeneous subgroups (strata) based on some characteristics of interest. Then, a random sample is selected from each stratum. Within each stratum, randomly selected elements are included in the sample. This ensures that the sample is representative of the population, and also allows for comparisons to be made between the different strata.

Question 11

In a local university, 40% of the students live in the dormitories.A random sample of 80 students is selected for a particular study.The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is
A) 0.4664
B) 0.9328
C) 0.9664
D) 0.0336

Accepted Answer

The distribution of the sample proportion can be approximated by a normal distribution due to the Central Limit Theorem as the sample size is sufficiently large (greater than 30) and the population is assumed to be normally distributed.

The mean of the sample proportion = population proportion = 0.40 
The standard deviation of the sample proportion = sqrt[(p*(1-p))/n] = sqrt[(0.40*0.60)/80] = 0.055

Now, we need to find the probability that the sample proportion is at least 0.30: 
P(p >= 0.30) = P(z >= (0.30-0.40)/0.055) 
                = P(z >= -1.82) 
                = 0.9664 (using a standard normal distribution table)

Therefore, the best choice is (C) 0.9664.

Question 12

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 mean always equals the population mean regardless of the sample size. This is a fundamental property of the mean and expected value.

Question 13

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 14

In a local university, 40% of the students live in the dormitories.A random sample of 80 students is selected for a particular study.The standard deviation of $\overline { \mathbf { p } }$ , known as the standard error of the proportion is approximately
A) 0.5477
B) 5.477
C) 0.05477
D) 54.77

Accepted Answer

The standard error of the proportion is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $p = 0.4$ and $n = 80$. This gives $\sqrt{\frac{0.4 \times 0.6}{80}} \approx 0.05477$.

Question 15

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

Accepted Answer

The desired situation is when the sampled population is identical to the targeted population as this ensures that the sample accurately represents the population and any findings or conclusions drawn from the sample can be generalised to the population as a whole. If the sampled population is larger, smaller, or more varied than the targeted population, this may lead to biased or inaccurate results.

Question 16

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 group of individuals or objects that we want to make inferences about based on the information we have from our sample or frame. Sampled population refers to the group of individuals or objects that we actually have data on. A frame is the list or method used to select the individuals or objects in our sample. Finite population refers to a population with a clearly defined and finite number of members, which is not necessarily relevant to the type of population we want to make inferences about.

Question 17

A random sample of 121 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 0.22 ounces.In this problem the 0.22 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

The 0.22 is the standard deviation of the population, not a calculated value from a sample, so it is a parameter. A statistic is a calculated value from a sample, so it is not the answer. The standard error of the mean is calculated by dividing the standard deviation by the square root of the sample size, so 0.22 is not the standard error of the mean. The average content of colognes in the long run cannot be determined from the information given, so it is not the answer.

Question 18

The standard deviation of $\bar { p }$ is referred to as the?
A)  standard proportion.
B)  sample mean proportion.
C)  deviated proportion.
D) standard error of the proportion.

Accepted Answer

The standard deviation of $\bar { p }$, the sample proportion, is known as the standard error of the proportion.

Question 19

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​
A) ​N has the same probability of being selected.
B) ​n has a probability of 0.5 of being selected.
C) ​n has a probability of 0.1 of being selected.
D) ​n has the same probability of being selected.

Accepted Answer

In a simple random sample, each possible sample of size n has the same probability of being selected from the population of size N.

Question 20

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

Accepted Answer

This is a method of systematic sampling where we choose every kth element from the population. It is important to randomly select the first element so that our sample is representative of the population. This method is more efficient than simple random sampling as it is less time-consuming and ensures adequate representation of the population.

Quiz 7: Sampling and Sampling Distributions

When the population has a normal distribution, the sampling distribution of $\bar x$ is normally distributed?

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

It is impossible to construct a frame for a(n)

In a local university, 40% of the students live in the dormitories.A random sample of 80 students is selected for a particular study.The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is

The standard deviation of $\bar x$ is referred to as 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.

Which of the following statements about cluster sampling is false?

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

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

In stratified random sampling,

In a local university, 40% of the students live in the dormitories.A random sample of 80 students is selected for a particular study.The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is

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

The standard error of the proportion will become larger as

In a local university, 40% of the students live in the dormitories.A random sample of 80 students is selected for a particular study.The standard deviation of $\overline { \mathbf { p } }$ , known as the standard error of the proportion is approximately

The desired situation is when

The population we want to make inferences about is the

A random sample of 121 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 0.22 ounces.In this problem the 0.22 is

The standard deviation of $\bar { p }$ is referred to as the?

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

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

Quiz 7: Sampling and Sampling Distributions

When the population has a normal distribution, the sampling distribution of xˉ \bar x xˉ is normally distributed?

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

It is impossible to construct a frame for a(n) ​

In a local university, 40% of the students live in the dormitories.A random sample of 80 students is selected for a particular study.The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is

The standard deviation of xˉ \bar x xˉ is referred to as 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.​

Which of the following statements about cluster sampling is false?​

The value of the ___________ is used to estimate the value of the population parameter​

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

In stratified random sampling,​