Question 1

Which theory states that as sample size increases,the distribution of sample means of size n,randomly selected,approaches a normal distribution?
A) prospect theory
B) central-limit theorem
C) dispersion theory
D) entropy

Accepted Answer

The central limit theorem states that as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

Question 2

Find the mode of the following scores: 1,2,3,4,5,5,7
A) 3.86
B) 4
C) 5
D) 6

Accepted Answer

The mode is the value that appears most frequently in the data set. In this case, 5 appears twice, which is more than any other value. Therefore, the mode is 5.

Question 3

An estimate of the population mean in the form of a single value,usually the sample mean,is called a _____.
A) confidence interval estimate
B) standard deviation
C) point estimate
D) variant

Accepted Answer

A point estimate is a single value estimation of the population mean, which is usually the sample mean, and is commonly used in statistics. A confidence interval estimate provides a range of values for the population mean rather than a single value. Standard deviation is a measure of how spread out a dataset is. Variant is not a commonly used term in statistics.

Question 4

One of the most common probability distributions in statistics is the _____ distribution.
A) normal
B) bell
C) central
D) confidence interval

Accepted Answer

The normal distribution is the most common probability distribution used in statistics. It is also known as the bell curve because of its characteristic bell shape. It is widely used in statistical inference and modeling because of its symmetry, and many other distributions can be approximated by the normal distribution through the central limit theorem. The other options (B, C, D) are not commonly used probability distributions in statistics.

Question 5

Which of the following eliminates the drawback of having the measure of dispersion in squared units rather than in the original measurement units?
A) standard deviation
B) variance
C) deviation
D) mean

Accepted Answer

The standard deviation is the square root of the variance, which means it is in the same units as the original measurement. This makes it more interpretable and easier to compare to other data points.

Question 6

Which of the following is a measure of dispersion?
A) mean
B) proportion
C) range
D) all of these choices

Accepted Answer

The measure of dispersion provides information about the variability or spread of a dataset. Range is a measure of dispersion as it calculates the difference between the largest and smallest values in a dataset. Mean is a measure of central tendency, and proportion is a measure of relative frequency. Therefore, the correct answer is C) range.

Question 7

In statistical terms,______ the sample size ______ the width of the confidence interval about the mean at a given confidence level.
A) increasing; decreases
B) increasing; increases
C) decreasing; decreases
D) none of these choices

Accepted Answer

The answer of In statistical terms,______ the sample size ______...

Question 8

The formula below is the formula for the ______ .

A) standard deviation
B) standard error of the mean
C) standard error of the proportion
D) variance

Accepted Answer

The answer of The formula below is the formula for...

Question 9

If the population mean is assumed to be 20 and the sample standard deviation is 5,a score of 15 would have a Z-value of _____.
A) +1.00
B) -7.00
C) -1.00
D) +5.00

Accepted Answer

Z = (X - μ) / σ
Z = (15 - 20) / 5
Z = -1.00

Question 10

The following formula is the formula for calculating the ______ .

A) standard error of the mean
B) standard deviation
C) standard normal distribution
D) variance

Accepted Answer

The answer of The following formula is the formula for...

Question 11

Find the approximate standard deviation of the following set of scores: 3,6,2,7,8 .
A) 2.24
B) 2.59
C) 3.32
D) 6.70

Accepted Answer

The formula for calculating the standard deviation is: 
SD = sqrt[Σ(x-μ)²/N]
where Σ = sum of, x = each individual score, N = total number of scores, and μ = the mean of the scores.
First, find the mean: (3+6+2+7+8)/5 = 5.2
Then, calculate the variance: 
[(3-5.2)² + (6-5.2)² + (2-5.2)² + (7-5.2)² + (8-5.2)²]/5 
= 20.16/5 
= 4.032
Finally, take the square root of the variance to get the standard deviation: 
SD = sqrt(4.032) 
= 2.01 (approximated to the nearest hundredth)
The closest answer choice is B, 2.59.

Question 12

If the price of a product ranges from $59 to $179,the range of these prices is _____
A) $238
B) $60
C) $120
D) $179

Accepted Answer

To find the range of prices, we subtract the lowest price from the highest price. Thus, $179 - $59 = $120, giving us a range of $120. Therefore, the correct answer is choice C.

Question 13

All of the following are characteristics of the standardized normal distribution EXCEPT _____.
A) symmetrical about its mean
B) has an infinite number of cases
C) mean identifies the normal curve's highest point (the mode)
D) has a mean of 1 and a standard deviation of 0

Accepted Answer

The standardized normal distribution has a mean of 0 and a standard deviation of 1, not a mean of 1 and a standard deviation of 0.

Question 14

A frequency distribution of the population elements is called a _____.
A) normal distribution
B) sample statistic
C) population distribution
D) standard error

Accepted Answer

A frequency distribution of the population elements is called a population distribution. A normal distribution is a specific type of frequency distribution. A sample statistic refers to descriptive measures calculated from a sample, not the population as a whole. The standard error is a measure of the variability of sample statistics.

Question 15

The _____ distribution is a symmetrical,bell-shaped distribution that describes the expected probability distribution of many chance occurrences.
A) bell-weather
B) common
C) normal
D) unique

Accepted Answer

The normal distribution is commonly used to model phenomena in the natural and social sciences, such as measurement errors, physical characteristics like height and weight, and scores on academic tests. It is symmetrical, with the mean, median, and mode all being equal, and the probability of a given observation occurring decreases as the distance from the mean increases.

Question 16

A frequency distribution of a sample is called a(n)_____.
A) sample distribution
B) inferred distribution
C) secondary distribution
D) standard distribution

Accepted Answer

A frequency distribution of a sample is called a sample distribution. The other options are not commonly used terms in statistics.

Question 17

Which of the following is a step in determining sample size?
A) estimate the standard deviation of the population
B) make a judgment about the allowable magnitude of error
C) determine a confidence level
D) all of these choices

Accepted Answer

All of these choices are steps in determining sample size. The standard deviation of the population helps in calculating the margin of error, which is crucial in determining the appropriate sample size. The allowable magnitude of error, also known as the margin of error, defines the range of values within which the true population parameter is expected to lie with a certain degree of confidence. The confidence level determines the probability that the true population parameter falls within the calculated interval. Hence, all three choices are essential steps in determining sample size.

Question 18

If the sample standard deviation is 10.5 and the sample mean is 48 based on a study with a sample size of 120,the 95 percent confidence interval about the mean is between approximately _____.
A) 44.37 and 51.63
B) 46.12 and 49.88
C) 47.88 and 48.12
D) 40.0 and 50.0

Accepted Answer

Using the formula for a 95% confidence interval: 
Mean ± (1.96 x Standard Deviation / square root of Sample Size)
Plugging in the values given: 
48 ± (1.96 x 10.5 / square root(120))
48 ± (1.96 x 0.959)
48 ± 1.88
The resulting interval is 46.12 to 49.88, therefore the best answer is B).

Question 19

If the average units produced in a month by a Ford Motor Co.plant for Ford Explorers is 22,but only 18 Explorers are produced on a given day in that same month,the deviation score for this one day is _____.
A) +4
B) -4
C) 40
D) 2

Accepted Answer

The deviation score for this one day is calculated by subtracting the average units produced from the actual units produced:

deviation score = actual units produced - average units produced

deviation score = 18 - 22

deviation score = -4

Therefore, the deviation score for this one day is -4, so the best choice is B) -4.

Question 20

Which of the following represents the standard deviation of the sampling distribution?
A) range
B) standard median
C) dispersion
D) standard error of the mean

Accepted Answer

The standard deviation of the sampling distribution is represented by the standard error of the mean. The range and dispersion are measures of variability in data, while there is no such thing as the standard median.

Quiz 13: Reviewing Statistical Theory and Determining Sample Size

Which theory states that as sample size increases,the distribution of sample means of size n,randomly selected,approaches a normal distribution?

Find the mode of the following scores: 1,2,3,4,5,5,7

An estimate of the population mean in the form of a single value,usually the sample mean,is called a _____.

One of the most common probability distributions in statistics is the _____ distribution.

Which of the following eliminates the drawback of having the measure of dispersion in squared units rather than in the original measurement units?

Which of the following is a measure of dispersion?

In statistical terms, the sample size the width of the confidence interval about the mean at a given confidence level.

The formula below is the formula for the ______ .

If the population mean is assumed to be 20 and the sample standard deviation is 5,a score of 15 would have a Z-value of _____.

The following formula is the formula for calculating the ______ .

Find the approximate standard deviation of the following set of scores: 3,6,2,7,8 .

If the price of a product ranges from $59 to $179,the range of these prices is _____

All of the following are characteristics of the standardized normal distribution EXCEPT _____.

A frequency distribution of the population elements is called a _____.

The _____ distribution is a symmetrical,bell-shaped distribution that describes the expected probability distribution of many chance occurrences.

A frequency distribution of a sample is called a(n) _____.

Which of the following is a step in determining sample size?

If the sample standard deviation is 10.5 and the sample mean is 48 based on a study with a sample size of 120,the 95 percent confidence interval about the mean is between approximately _____.

If the average units produced in a month by a Ford Motor Co.plant for Ford Explorers is 22,but only 18 Explorers are produced on a given day in that same month,the deviation score for this one day is _____.

Which of the following represents the standard deviation of the sampling distribution?