Assistance for AMU MATH 120 Intro to statistics quiz 2 week 2 answers American Military University is available at Domyclass

Table of Contents

#### MATH 120 AMU QUIZ 2 question 1

Consider the mode, median, and mean.

(a) Which average represents the middle value of a data distribution?

mode

median

mean

(b) Which average represents the most frequent value of a data distribution?

mode

median

mean

.

(c) Which average takes all the specific values into account?

mode

median

mean

#### MATH 120 AMU QUIZ 2 question 2

What symbol is used for the arithmetic mean when it is a sample statistic? What symbol is used when the arithmetic mean is a population parameter?

statistic, x bar; parameter, x bar

statistic, x bar; parameter, μ

statistic, μ; parameter, x bar

statistic, μ; parameter, μ

MATH 120 AMU QUIZ 2 question 3

Find the mean, median, and mode of the data set.

8 4 7 4 5

mean (Enter a number.)

median (Enter an exact number.)

mode (Enter an exact number.)

#### MATH 120 AMU QUIZ 2 question 4

How large is a wolf pack? The following information is from a random sample of winter wolf packs. Winter pack size are given below. Compute the mean, median, and mode for the size of winter wolf packs. (For each answer, enter a number. Round your answers to one decimal place.)

1 9 6 4 6 6 1 3 2

12 2 14 3 3 1 7 6 7

mean

median

mode

#### MATH 120 AMU QUIZ 2 question 5

Find the weighted average of a data set where 10 has a weight of 5, 30 has a weight of 2, and 50 has a weight of 3. (Enter an exact number.)

#### MATH 120 AMU QUIZ 2 question 6

What symbol is used for the standard deviation when it is a sample statistic? What symbol is used for the standard deviation when it is a population parameter?

Sample statistic: σ. Population parameter: s.

For both, s is used.

For both, σ is used.

Sample statistic: s. Population parameter: σ.

#### MATH 120 AMU QUIZ 2 question 7

Consider the data set.

2, 3, 4, 6, 8

(a) Find the range. (Enter an exact number.)

(b) Use the defining formula to compute the sample standard deviation s. (Enter a number. Round your answer to two decimal places.)

(c) Use the defining formula to compute the population standard deviation σ. (Enter a number. Round your answer to two decimal places.)

#### MATH 120 AMU QUIZ 2 question 8

One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80.

(a) If a data set has mean 70 and standard deviation 5, is 80 a suspect outlier?

No, since 80 is more than 2.5 standard deviations above the mean.

Yes, since 80 is more than 2.5 standard deviations above the mean.

No, since 80 is less than 2.5 standard deviations above the mean.

Yes, since 80 is less than 2.5 standard deviations above the mean.

(b) If a data set has mean 70 and standard deviation 3, is 80 a suspect outlier?

No, since 80 is more than 2.5 standard deviations above the mean.

Yes, since 80 is more than 2.5 standard deviations above the mean.

No, since 80 is less than 2.5 standard deviations above the mean.

Yes, since 80 is less than 2.5 standard deviations above the mean.

#### MATH 120 AMU QUIZ 2 question 9

Given the sample data.

x: 23, 19, 13, 30, 27

(a) Find the range. (Enter an exact number.)

(b) Verify that Σx = and Σx2 = . (For each answer, enter an exact number.)

Σx =

Σx2 =

(c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s. (For each answer, enter a number. Round your answers to two decimal places.)

s2 =

s =

(d) Use the defining formulas to compute the sample variance s2 and sample standard deviation s. (For each answer, enter a number. Round your answers to two decimal places.)

s2 =

s =

(e) Suppose the given data comprise the entire population of all x values. Compute the population variance σ2 and population standard deviation σ. (For each answer, enter a number. Round your answers to two decimal places.)

σ2 =

σ =

#### MATH 120 AMU QUIZ 2 question 10

Consider sample data with x bar = 4 and s = 2. (For each answer, enter an exact number.)

(a) Compute the coefficient of variation (as a percent).

(b) Compute a 75% Chebyshev interval around the sample mean.

Lower Limit

.

Upper Limit

#### MATH 120 AMU QUIZ 2 question 11

Describe the relationship between two variables when the correlation coefficient r is one of the following.

(a) near −1

strong negative linear correlation

weak or no linear correlation

weak negative linear correlation

weak positive linear correlation

strong positive linear correlation

(b) near 0

weak or no linear correlation

strong negative linear correlation

strong positive linear correlation

weak negative linear correlation

weak positive linear correlation

(c) near 1

weak negative linear correlation

weak or no linear correlation

strong positive linear correlation

strong negative linear correlation

weak positive linear correlation

#### MATH 120 AMU QUIZ 2 question 12

Look at the following diagrams. Which diagrams show high linear correlation, moderate or low linear correlation, or no linear correlation? (There are three diagrams. You will be presented the diagrams one at a time.)

Consider diagram (a). The diagram shows 10 points plotted in the first quadrant. There are points plotted in the bottom left of the graph. They continue to be plotted diagonally toward the top right corner of the graph. The points are somewhat scattered.

no

moderate or low

high

Consider diagram (b). The diagram shows 24 points plotted in the first quadrant. There are points plotted in the bottom left corner close together. The points continue to be plotted in a steep positive direction until there is a peak about two-thirds of the height of the graph. The points continue to be plotted in a negative direction reaching a minimum near the bottom of the graph. Then the points again are plotted in a steep positive direction, ending with points near the top right corner of the graph. The points show very little scatter.

moderate or low

no

high

Consider diagram (c). The diagram shows 14 points plotted in the first quadrant. There are points plotted in the bottom left of the graph. They continue to be plotted diagonally toward the top right corner of the graph. The points are all plotted close together with very little scatter.

moderate or low

no

high

#### MATH 120 AMU QUIZ 2 question 13

How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms).

x 3 6 12 18 24

y 60 95 140 170 189

(a) Make a scatter diagram of the data and visualize the line you think best fits the data. (Submit a file with a maximum size of 1 MB.)

(b) Would you say the correlation is low, moderate, or strong?

low

moderate

strong

Would you say the correlation is positive or negative?

positive

negative

(c) Use a calculator to verify that Σ(x) = 63, Σ(x2) = 1089, Σ(y) = 654, Σ(y2) = 96,846, and Σ(x y) =

Compute r. (Enter a number. Round your answer to three decimal places.)

As x increases from 3 to 24 months, does the value of r imply that y should tend to increase or decrease? Explain your answer.

Given our value of r, y should tend to decrease as x increases.

Given our value of r, y should tend to remain constant as x increases.

Given our value of r, y should tend to increase as x increases.

Given our value of r, we can not draw any conclusions for the behavior of y as x increases.

#### MATH 120 AMU QUIZ 2 question 14

Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Let x be a variable that represents student enrollment (in thousands) on a university campus, and let y be a variable that represents the number of burglaries in a year on the university campus. A random sample of n = 8 universities in California gave the following information about enrollments and annual burglary incidents.

x 13.1 31.8 24.5 14.3 7.5 27.7 16.2 20.1

y 24 75 39 23 15 30 15 25

(a) Make a scatter diagram of the data. Then visualize the line you think best fits the data. (Submit a file with a maximum size of 1 MB.)

(b) Use a calculator to verify that Σ(x) = 155.2, Σ(x2) = 3477.58, Σ(y) = 246, Σ(y2) = 10226 and Σ(x y) = 5672.8.

Compute r. (Enter a number. Round to 3 decimal places.)

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

Given our value of r, we can not draw any conclusions for the behavior of y as x increases.

Given our value of r, y should tend to increase as x increases.

Given our value of r, y should tend to decrease as x increases.

Given our value of r, y should tend to remain constant as x increases.

#### MATH 120 AMU QUIZ 2 question 15

In the least-squares line ŷ = 5 − 8x, what is the value of the slope? (Enter an exact number.)

When x changes by 1 unit, by how much does ŷ change?

When x increases by 1 unit, ŷ decreases by 8 units.

When x increases by 1 unit, ŷ increases by 8 units.

When x decreases by 1 unit, ŷ decreases by 8 units.

When x increases by 1 unit, ŷ decreases by −8 units.

#### MATH 120 AMU QUIZ 2 question 16

If two variables have a negative linear correlation, is the slope of the least-squares line positive or negative?

positive

negative

#### MATH 120 AMU QUIZ 2 question 17

You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms).

x 1 5 11 16 26 36

y 39 47 73 100 150 200

Complete parts (a) through (e), given Σx = 95, Σy = 609, Σx2 = 2375, Σy2 = 81,559, Σx y = 13,777, and r ≈ 0.997.

(a)

Make a scatter diagram of the data. (Select the correct graph.)

A scatter diagram with 6 points is graphed on the x y coordinate plane. The points are located at (1, 29), (5, 37), (11, 63), (16, 90), (26, 140), (36, 190). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right. A scatter diagram with 6 points is graphed on the x y coordinate plane. The points are located at (1, 39), (5, 47), (11, 73), (16, 100), (26, 150), (36, 200). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right. A scatter diagram with 6 points is graphed on the x y coordinate plane. The points are located at (3, 29), (7, 37), (13, 63), (18, 90), (28, 140), (38, 190). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right. A scatter diagram with 6 points is graphed on the x y coordinate plane. The points are located at (3, 39), (7, 47), (13, 73), (18, 100), (28, 150), (38, 200). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right.

.

(b)

Verify the given sums Σx, Σy, Σx2, Σy2, Σx y, and the value of the sample correlation coefficient r. (For each answer, enter a number. Round your value for r to three decimal places.)

Σx =

95

Σy =

609

Correct: Your answer is correct.

Σx2 =

2375

Correct: Your answer is correct.

Σy2 =

81,559

Correct: Your answer is correct.

Σx y =

13,777

Correct: Your answer is correct.

r =

0.997

Correct: Your answer is correct.

(c)

Find x bar, and y bar. Then find the equation of the least-squares line y hat = a + b x. (For each answer, enter a number. Round your answers for x bar and y bar to two decimal places. Round your answers for a and b to three decimal places.)

x bar = x bar =

y bar = y bar =

y hat = value of a coefficient

+ value of b coefficient

x

(d)

Graph the least-squares line. Be sure to plot the point (x bar, y bar) as a point on the line. (Select the correct graph.)

A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 132). The line enters the window at approximately y = 56 on the positive y axis, goes up and right, passes through the approximate point (15.8, 132), and exits the window in the first quadrant. A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 102). The line enters the window at approximately y = 26 on the positive y axis, goes up and right, passes through the approximate point (15.8, 102), and exits the window in the first quadrant. A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 132). The line enters the window at approximately y = 201 on the positive y axis, goes down and right, passes through the approximate point (15.8, 132), and exits the window in the first quadrant. A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 102). The line enters the window at approximately y = 171 on the positive y axis, goes down and right, passes through the approximate point (15.8, 102), and exits the window at approximately x = 39.1 on the positive x axis.

(e)

Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (For each answer, enter a number. Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =

explained =

unexplained =

(f)

The calves you want to buy are 24 weeks old. What does the least-squares line predict for a healthy weight (in kg)? (Enter a number. Round your answer to two decimal places.)

#### MATH 120 AMU QUIZ 2 question 18

Consider the following ordered data.

12 15 15 16 17 17 18 19 20

(a) Find the low, Q1, median, Q3, and high. (For each answer, enter a number.)

low

Q1

.

median

.

Q3

high

(b) Find the interquartile range. (Enter a number.)

(c) Make a box-and-whisker plot. (Select the correct graph.)

#### MATH 120 AMU QUIZ 2 question 19

At one hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were as follows.

29 8 11 20 31 42 33 48 18 14

13 29 35 32 34 17 26 37 14 42

Make a box-and-whisker plot of the data. (Select the correct graph.)

Find the interquartile range. (Enter an exact number.)

IQR =