Question

1. Suppose on a sample of Montanans it is found the mean salary is equal to 30,000. When we use a statistic like this to simply describe a sample, this is an example of:

a) an inferential statistic

b) a descriptive statistic

c) a sample median

d) random sampling

e) b and c





2. If we collect observations on 100 people, and measure their IQ, the 100 observations is:



a) a sample

b) a population

c) a sample with likely no variability

d) a or b are possibilities, depending on the scope of the investigation

e) a variable





Suppose the trace of a matrix is equal to 10. If this matrix is also an identity matrix, how many rows must the matrix have?



10

equal to the number of columns of the matrix

0

a and b

impossible to say without further information











4. If it is universally known in general that all cats have four legs, then the conclusion that your particular cat has four legs is an example of:



inductive inference

deductive inference

statistical inference

d) a mathematical function

e) none of the above





5. Suppose you have values on variable equal to , and wish to compute a measure of variation from the mean. Without knowing what the exact values of the variable are, which of the following measures will necessarily generate a positive number (which is of course different from zero) regardless of the values for ?



a) the sum of absolute deviations from the mean

b) the sum of deviations from the mean

c) the sum of squared deviations from the mean

d) the standard deviation

e) a and c

f) none of the above





6. One common interpretation of the derivative in mathematics is:



a quadratic function

an instantaneous rate of change

the limit of a linear function

none of the above





7. Consider the numbers 1, 2, 3, 4 assigned to values of a variable. The variable being measured is most likely:



a) quantitative

b) qualitative

c) one for which computing the standard deviation would likely be appropriate

d) one for which computing the median would definitely be inappropriate

e) a and c









8. Integration in calculus is generally used for:



computing the rate of change of one variable with respect to another

computing areas under curves

computing areas in rectangles only

none of the above





9. If the mean of some data set is equal to 10, then this necessarily implies:



a) 1/2 of the scores fall above and below the mean of 10

b) the score of 10 must exist in the actual data set of recorded values

c) the variance of the data is probably negative

d) the standard deviation cannot be greater than 10

e) the distribution is normal

f) none of the above





10. If you compute the arithmetic mean, the sum of deviations of scores from that mean are always equal to:



a) 1

b) 0

c) 0 or a positive number

d) a squared number

e) none of the above

Answer 1

The mean salary figure represents a descriptive statistic. A collection of 100 IQ observations is a sample, and deduction from a universal statement, like all cats having four legs, is deductive inference. The derivative is an instantaneous rate of change, and integration in calculus typically involves finding areas under curves.

Step-by-step explanation:

The mean salary described for a sample of Montanans, being used purely for descriptive purposes, is an example of descriptive statistics. When we calculate measures like the mean or median for a sample, we're summarizing the data without making conclusions about a larger population.

The 100 IQ observations would constitute a sample, as they represent a subset of the entire population's IQ. When we generalize from a sample about the population, we're dealing with inferential statistics.

The trace of an identity matrix is equal to the sum of its diagonal elements, which are all 1s. Hence, if the trace is 10, the matrix must be 10x10, implying it has 10 rows.

Concluding that your cat has four legs, based on the universal knowledge that all cats do, is an example of deductive inference, where a general statement is used to derive a specific case.

The only measures that will always generate a positive number, regardless of data values, when assessing variation from the mean are the sum of absolute deviations from the mean and the sum of squared deviations from the mean.

The derivative represents an instantaneous rate of change, showing how one quantity varies instantaneously as another quantity changes.

The variable assigned the numbers 1, 2, 3, and 4 is likely quantitative, and computing the standard deviation would be appropriate to measure its variance.

In calculus, integration is commonly used for calculating the areas under curves, which may represent accumulated quantities or distributions.

If the mean of a dataset is 10, it doesn't necessarily imply any specific distribution of scores around that mean; therefore, none of the given statements are necessarily true.

When you compute an arithmetic mean, the sum of deviations of scores from that mean is always equal to 0. This is because the mean is the balancing point of the data.

Answer 2

1. Suppose on a sample of Montanans it is found the mean salary is equal to 30,000. When we use a statistic like this to simply describe a sample, this is an example of:

a) an inferential statistic

b) a descriptive statistic

c) a sample median

d) random sampling

e) b and c

2. If we collect observations on 100 people, and measure their IQ, the 100 observations is:

a) a sample

b) a population

c) a sample with likely no variability

d) a or b are possibilities, depending on the scope of the investigation

e) a variable

Suppose the trace of a matrix is equal to 10. If this matrix is also an identity matrix, how many rows must the matrix have?

10

equal to the number of columns of the matrix

0

a and b

impossible to say without further information

4. If it is universally known in general that all cats have four legs, then the conclusion that your particular cat has four legs is an example of:

inductive inference

deductive inference

statistical inference

d) a mathematical function

e) none of the above

5. Suppose you have values on variable equal to , and wish to compute a measure of variation from the mean. Without knowing what the exact values of the variable are, which of the following measures will necessarily generate a positive number (which is of course different from zero) regardless of the values for ?

a) the sum of absolute deviations from the mean

b) the sum of deviations from the mean

c) the sum of squared deviations from the mean

d) the standard deviation

e) a and c

f) none of the above

6. One common interpretation of the derivative in mathematics is:

a quadratic function

an instantaneous rate of change

the limit of a linear function

none of the above

7. Consider the numbers 1, 2, 3, 4 assigned to values of a variable. The variable being measured is most likely:

a) quantitative

b) qualitative

c) one for which computing the standard deviation would likely be appropriate

d) one for which computing the median would definitely be inappropriate

e) a and c

8. Integration in calculus is generally used for:

computing the rate of change of one variable with respect to another

computing areas under curves

computing areas in rectangles only

none of the above

9. If the mean of some data set is equal to 10, then this necessarily implies:

a) 1/2 of the scores fall above and below the mean of 10

b) the score of 10 must exist in the actual data set of recorded values

c) the variance of the data is probably negative

d) the standard deviation cannot be greater than 10

e) the distribution is normal

f) none of the above

10. If you compute the arithmetic mean, the sum of deviations of scores from that mean are always equal to:

a) 1

b) 0

c) 0 or a positive number

d) a squared number

e) none of the above