Question 1

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18,respectively.The distribution of the population is unknown.The mean and the standard error of the mean are
A)200 and 18
B)81 and 18
C)9 and 2
D)200 and 2

Accepted Answer

The mean of the population is 200, which will also be the mean of the sampling distribution of the mean.
The standard error of the mean (SEM) will be the standard deviation of the sampling distribution, which is equal to the population standard deviation divided by the square root of the sample size:
SEM = 18 / sqrt(81) = 2.

Therefore, the answer is D - 200 and 2.

Question 2

A simple random sample of 5 observations from a population containing 400 elements was taken,and the following values were obtained.

A point estimate of the mean is
A)400
B)18
C)20
D)10

Accepted Answer

The point estimate of the mean can be calculated by taking the average of the sample.

(16 + 18 + 20 + 19 + 17) / 5 = 18

Therefore, the best choice is B.

Question 3

A simple random sample of size n from an infinite population of size N is to be selected.Each possible sample should have
A)the same probability of being selected
B)a probability of 1/n of being selected
C)a probability of 1/N of being selected
D)a probability of N/n of being selected

Accepted Answer

The answer of A simple random sample of size n...

Question 4

The purpose of statistical inference is to provide information about the
A)sample based upon information contained in the population
B)population based upon information contained in the sample
C)population based upon information contained in the population
D)mean of the sample based upon the mean of the population

Accepted Answer

Statistical inference involves using information collected from a sample to make conclusions or predictions about a population. Therefore, the purpose of statistical inference is to provide information about the population based on information contained in the sample.

Question 5

Random samples of size 49 are taken from a population that has 200 elements,a mean of 180,and a variance of 196.The distribution of the population is unknown.The mean and the standard error of the mean are
A)180 and 24.39
B)180 and 28
C)180 and 2
D)180 and 1.74

Accepted Answer

The answer of Random samples of size 49 are taken...

Question 6

Random samples of size 525 are taken from an infinite population whose population proportion is 0.3.The standard deviation of the sample proportions (i.e. ,the standard error of the proportion)is
A)0.0004
B)0.2100
C)0.3000
D)0.0200

Accepted Answer

The formula for the standard error of the proportion is $\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the population proportion and $n$ is the sample size. Plugging in $p=0.3$ and $n=525$, we get $\sqrt{\frac{0.3(1-0.3)}{525}} \approx 0.019976 \approx 0.0200$. Therefore, the answer is D.

Question 7

A population has a mean of 80 and a standard deviation of 7.A sample of 49 observations will be taken.The probability that the sample mean will be larger than 82 is
A)0.5228
B)0.9772
C)0.4772
D)0.0228

Accepted Answer

We need to use the Central Limit Theorem (CLT) to solve this problem. According to CLT, the sampling distribution of the sample means is approximately normal with mean μ and standard deviation σ/√n, where μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, we have μ = 80, σ = 7, and n = 49. Therefore, the sampling distribution of the sample means is approximately normal with mean 80 and standard deviation 7/√49 = 1.

Now, we want to find the probability that the sample mean will be larger than 82. We can standardize the sample mean by using the z-score formula:

z = (x̄ - μ) / (σ/√n)

where x̄ is the sample mean. Plugging in the values, we get:

z = (82 - 80) / (1) = 2

We want to find the probability that z is greater than 2. This is equivalent to finding the area to the right of z = 2 under the standard normal distribution curve.

Using a standard normal distribution table or a calculator, we find that the probability is 0.0228 (rounded to four decimal places).

Therefore, the answer is D) 0.0228.

Question 8

A sample of 400 observations will be taken from an infinite population.The population proportion equals 0.8.The probability that the sample proportion will be greater than 0.83 is
A)0.4332
B)0.9332
C)0.0668
D)0.5668

Accepted Answer

We can use the central limit theorem to approximate the sampling distribution of the sample proportion as normal with mean equal to population proportion (p) and standard deviation equal to the square root of (p*(1-p)/n), where n is the sample size. Substituting the given values, we get a normal distribution with mean 0.8 and standard deviation 0.02. To find the probability that the sample proportion will be greater than 0.83, we need to find the z-score corresponding to this proportion:

z = (0.83 - 0.8) / 0.02 = 1.5

Using a standard normal table or calculator, we can find that the probability of getting a z-score greater than 1.5 is approximately 0.0668. Therefore, the answer is C.

Question 9

For a population with any distribution,the form of the sampling distribution of the sample mean is
A)sometimes normal for all sample sizes
B)sometimes normal for large sample sizes
C)always normal for all sample sizes
D)always normal for large sample sizes

Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will approach a normal distribution as the sample size becomes large, regardless of the shape of the population distribution.

Question 10

A random sample of 150 people was taken from a very large population.Ninety of the people in the sample were female.The standard error of the proportion is
A)0.0016
B)0.2400
C)0.1600
D)0.0400

Accepted Answer

The answer of A random sample of 150 people was...

Question 11

From a population of 500 elements,a sample of 225 elements is selected.It is known that the variance of the population is 900.The standard error of the mean is approximately
A)1.1022
B)2
C)30
D)1.4847

Accepted Answer

The formula for standard error of the mean is:

SE = $\frac{\sigma}{\sqrt{n}}$

where $\sigma$ is the population standard deviation, and n is the sample size.

We know that the variance of the population is 900, so the standard deviation is:

$\sigma = \sqrt{900} = 30$

And the sample size is 225.

Plugging these values into the formula, we get:

SE = $\frac{30}{\sqrt{225}}$

SE = $\frac{30}{15}$

SE = 2

Therefore, the answer is choice D: 2.

Question 12

A sample of 24 observations is taken from a population that has 150 elements.The sampling distribution of  Is
A)approximately normal because  Is always approximately normally distributed
B)approximately normal because the sample size is large in comparison to the population size
C)approximately normal because of the central limit theorem
D)normal if the population is normally distributed

Accepted Answer

The answer of A sample of 24 observations is taken...

Question 13

A sample of 92 observations is taken from an infinite population.The sampling distribution of  Is approximately
A)normal because  Is always approximately normally distributed
B)normal because the sample size is small in comparison to the population size
C)normal because of the central limit theorem
D)None of these alternatives is correct.

Accepted Answer

The central limit theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. Therefore, the sampling distribution of the sample mean in this case is approximately normal because the sample size is relatively large (92 observations). Option A is incorrect because the fact that the population is infinite does not guarantee a normal sampling distribution. Option B is incorrect because the sample size is not small in comparison to the population size. Option D is incorrect as option C is the correct explanation for this problem.

Question 14

A simple random sample of 64 observations was taken from a large population.The sample mean and the standard deviation were determined to be 320 and 120 respectively.The standard error of the mean is
A)1.875
B)40
C)5
D)15

Accepted Answer

The answer of A simple random sample of 64 observations...

Question 15

The number of random samples (without replacement)of size 3 that can be drawn from a population of size 5 is
A)15
B)10
C)20
D)125

Accepted Answer

The answer of The number of random samples (without replacement)of...

Question 16

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the
A)approximation theorem
B)normal probability theorem
C)central limit theorem
D)central normality theorem

Accepted Answer

The central limit theorem states that as the sample size increases, the distribution of sample means or sample proportions approaches a normal distribution. Therefore, we can use the normal distribution to approximate the sampling distribution of sample means and sample proportions when the sample size is large. Choice A is not a commonly used term, choice B is not specific enough, and choice D is not a recognized term in statistics.

Question 17

A simple random sample of 28 observations was taken from a large population.The sample mean equaled 50.Fifty is a
A)population parameter
B)biased estimate of the population mean
C)sample parameter
D)point estimate

Accepted Answer

The sample mean of 50 is a point estimate of the population mean, as it is based on a single sample and is used to estimate the population parameter of the mean.

Question 18

A population has a mean of 180 and a standard deviation of 24.A sample of 64 observations will be taken.The probability that the sample mean will be between 183 and 186 is
A)0.1359
B)0.8185
C)0.3413
D)0.4772

Accepted Answer

The answer of A population has a mean of 180...

Question 19

Random samples of size 36 are taken from an infinite population whose mean and standard deviation are 20 and 15,respectively.The distribution of the population is unknown.The mean and the standard error of the mean are
A)36 and 15
B)20 and 15
C)20 and 0.417
D)20 and 2.5

Accepted Answer

The mean of the population is represented by μ = 20, and the standard deviation of the population is represented by σ = 15. The standard error of the mean is represented as σ/√n, where n is the sample size. In this case, n = 36. Therefore, the standard error of the mean is:

σ/√n = 15/√36 = 15/6 = 2.5

So, the mean of the sample is 20, and the standard error of the mean is 2.5. Therefore, the best choice is D.

Question 20

There are 6 children in a family.The number of children defines a population.The number of simple random samples of size 2 (without replacement)which are possible equals
A)12
B)15
C)3
D)16

Accepted Answer

The answer of There are 6 children in a family.The...

Quiz 7: Sampling and Sampling Distributions

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18,respectively.The distribution of the population is unknown.The mean and the standard error of the mean are

A simple random sample of 5 observations from a population containing 400 elements was taken,and the following values were obtained. A point estimate of the mean is

A simple random sample of size n from an infinite population of size N is to be selected.Each possible sample should have

The purpose of statistical inference is to provide information about the

Random samples of size 49 are taken from a population that has 200 elements,a mean of 180,and a variance of 196.The distribution of the population is unknown.The mean and the standard error of the mean are

Random samples of size 525 are taken from an infinite population whose population proportion is 0.3.The standard deviation of the sample proportions (i.e. ,the standard error of the proportion) is

A population has a mean of 80 and a standard deviation of 7.A sample of 49 observations will be taken.The probability that the sample mean will be larger than 82 is

A sample of 400 observations will be taken from an infinite population.The population proportion equals 0.8.The probability that the sample proportion will be greater than 0.83 is

For a population with any distribution,the form of the sampling distribution of the sample mean is

A random sample of 150 people was taken from a very large population.Ninety of the people in the sample were female.The standard error of the proportion is

From a population of 500 elements,a sample of 225 elements is selected.It is known that the variance of the population is 900.The standard error of the mean is approximately

A sample of 24 observations is taken from a population that has 150 elements.The sampling distribution of Is

A sample of 92 observations is taken from an infinite population.The sampling distribution of Is approximately

A simple random sample of 64 observations was taken from a large population.The sample mean and the standard deviation were determined to be 320 and 120 respectively.The standard error of the mean is

The number of random samples (without replacement) of size 3 that can be drawn from a population of size 5 is

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the

A simple random sample of 28 observations was taken from a large population.The sample mean equaled 50.Fifty is a

A population has a mean of 180 and a standard deviation of 24.A sample of 64 observations will be taken.The probability that the sample mean will be between 183 and 186 is

Random samples of size 36 are taken from an infinite population whose mean and standard deviation are 20 and 15,respectively.The distribution of the population is unknown.The mean and the standard error of the mean are

There are 6 children in a family.The number of children defines a population.The number of simple random samples of size 2 (without replacement) which are possible equals