Statistics The Exploration & Analysis of Data, International Edition, 7th Edition By Roxy Peck - Test Bank

Statistics The Exploration & Analysis of Data, International Edition, 7th Edition By Roxy Peck – Test Bank

 

Instant Download – Complete Test Bank With Answers

 

 

Sample Questions Are Posted Below

 

Chapter 5:  Summarizing Bivariate Data

Section 5.1-5.2

 

Name ___________________________

 

 

1. What is it that the Pearson correlation coefficient quantifies?

 

 

 

 

 

 

 

 

 

2. If a scatter plot exhibits a strong negative relationship, what can be said about the value of the quantity, ?

 

 

 

 

 

 

 

 

3. One of the properties of Pearson’s r is: “The value of r does not depend on the unit of measurement for either variable.”   In your own words, what does this mean?

 

4. The breeding success of birds that nest on the ground can be affected by the depth of winter snow in high altitudes. The plot below relates the percentage of White-tailed Ptarmigan hens hatching at least one egg, to the amount of snowfall in the Sierra Nevadas that winter.

	%NestSuccess  Vs.  SnowDepth(cm)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. a) The least squares best fit line is . Graph this line using the axes above.  Show any calculations in the space below.

 

 

 

 

 

 

 

 

 

 

 

 

 

1. b) The least squares line is the line that minimizes the sum of the squared residuals. On the graph above pick 2 points and sketch the residuals associated with those points.

 

 

5. The early human ancestors were similar in shape to most large primates. The data below are average male hind limb and forelimb lengths for different species of early homonins (humans and their ancestors.)  The relatively short hind limbs are thought to represent evolutionary specialization for vertical climbing.

 

                                    Hind limb and Forelimb lengths

 

Hind limb Length (mm)	Forelimb Length (mm)
471	458
361	514
399	581
557	739
553	553
574	614
857	595
698	762

 

1. a) What is the value of the correlation coefficient for these data?

 

 

 

1. b) What is the equation of the least squares line describing the relationship between

x = hind limb length and y = forelimb length.

 

 

 

 

 

 

1. c) Suppose these species are representative of species of early human ancestors. If a new homonin species dating from about the same time were to be discovered with an average hind limb length of 500 mm, what would you predict to be the average forelimb length of this species?

 

Chapter 5:  Summarizing Bivariate Data

Section 5.3-5.4a

 

Name ___________________________

 

 

1. The Des Moines Register recently reported the ratings of high school sportsmanship as compiled by the Iowa High School Athletic Association. For each school the participants and coaches were rated by referees, where 1 = superior, and 5 = unsatisfactory.  A regression analysis of the average scores given to football players and coaches is shown below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. a) Interpret the value of the correlation between the ratings of coaches and participants.

 

 

 

 

1. b) Interpret the value of the coefficient of determination.

 

 

 

 

1. c) Interpret the value of the standard deviation about the least squares line.

 

 

 

 

2. As early as 3 years of age, children begin to show preferences for playing with members of their own sex, and report having more same-sex than opposite-sex friends. In a study of 3rd and 4th graders’ views on 48 personality traits, children were asked to rate on a “5-point” scale:

 

-2 = “someone possessing that trait is probably a boy”

-1 = “someone possessing that trait might be a boy”

0 = “can’t tell”

1 = “someone possessing that trait might be a girl”

2 = “someone possessing that trait is probably a girl”

 

A plot of the data is presented below.  A single point represents the (average girls’ rating, average boys’ rating) for a given trait.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. a) Circle the single point which represents the most influential observation. What aspect of this point makes it the most influential?

 

 

 

 

 

 

 

1. b) Suppose a personality trait similar to those used in the survey were given a 0.0 rating (“can’t tell”) by the girls.  The predicted boys’ average rating would be closest to which of the 5 categories described above?

 

 

 

 

 

 

 

 

 

 

1. c) The traits plotted above are those the researchers believe are “positive” traits, such as “mature,” “honest,” and “polite.”  The researchers thought that on average girls would rate these positive traits as characteristic of girls to a greater extent than boys would.  What aspects of the plot and/or regression analysis presented above are consistent with this thinking?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3. A common statistical method for estimating a population size assumes each member of the population has an equal probability of being captured. To assess this assumption for crocodile populations, investigators repeatedly sampled sections of rivers in Australia.  Crocodile lengths were measured in size classes.  Crocs 0.0 – 0.3 meters in length are in size class 1, 0.3 – 0.6 meters in length are size class 2, etc.  The normal maximum adult length is in a class size of 9 or 10.   The investigators fit a quadratic function relating the probability of capture and the size class of captured crocodiles.  The output from their analysis is shown below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) What proportion of the variability in probability of capture is explained by the crocodile’s size class?

 

 

 

(b) Some biologists speculate that as crocodiles grow they become more wary of humans, and are more difficult to detect in the wild.   Support or refute this belief by appealing to the analysis above.

 

 

 

 

 

 

 

 

 

 

 

 

4. Assessing the goodness of fit of a regression line involves considering several things, and no single characteristic of data is sufficient for a good assessment. Consider the characteristics below.  How does each contribute to an assessment of fit?  That is, for each piece of information, what characteristic would indicate a “good” best-fit line?

 

1. a) The shape of the scatter plot

 

 

 

 

 

 

 

 

 

1. b) The correlation coefficient

 

 

 

 

 

 

 

 

 

1. c) The standard deviation of the residuals

 

 

 

 

 

 

 

 

 

1. d) The coefficient of determination

 

Chapter 5:  Summarizing Bivariate Data

Section 5.3-5.4a

 

Name ___________________________

 

 

1. The Des Moines Register recently reported the ratings of high school sportsmanship as compiled by the Iowa High School Athletic Association. For each school the spectators and participants were rated by referees, where 1 = superior, and 5 = unsatisfactory.  A regression analysis of the average scores given to wrestling spectators and wrestlers is shown below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. a) Interpret the value of the correlation between the ratings of spectators and wrestlers?

 

 

 

 

1. b) Interpret the value of the coefficient of determination.

 

 

 

 

1. c) Interpret the value of the standard deviation about the least squares line?

 

 

 

 

 

 

2. Children begin to show preferences for playing with members of their own sex as early as 3 years of age, and report having more same-sex than opposite-sex friends. In a study of 3rd and 4th graders’ views on 48 personality traits, children were asked to rate on a “5-point” scale:

 

-2 = “someone possessing that trait is probably a boy”

-1 = “someone possessing that trait might be a boy”

0 = “can’t tell”

1 = “someone possessing that trait might be a girl”

2 = “someone possessing that trait is probably a girl”

 

A plot of the data is presented below.  A single point (ordered pair) represents the (average girls’ rating, average boys’ rating) for that trait.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. a) Circle the single point that represents the most influential observation. What aspect of this point makes it the most influential?

 

 

 

 

 

 

 

1. b) Suppose a personality trait similar to those used in the survey was given a 0.0 rating (“can’t tell”) by the girls.  The predicted boys’ average rating would be closest to which of the 5 categories described above?

 

 

 

 

 

 

 

 

 

 

1. c) The traits plotted above are those the researchers believe are “positive” traits, such as “mature,” “honest,” and “polite.”  The researchers thought that on average girls would rate these positive traits as characteristic of girls to a greater extent than boys would rate these traits.  Are the data above consistent with the researchers’ thinking?   Explain your reasoning, using appropriate statistical terminology.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3. Polar bear cubs are born in the winter in dens, and live off the fat stores of the mother even after leaving the den. Therefore maternal weight is an important factor in successful reproduction of polar bears.  In a recent spring, 261 adult females with 492 cubs were captured as they left their dens, and the mothers’ weight and ages were determined. A quadratic fit of the maternal weight in kilograms to age in years resulted in the regression analysis below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. a) On average, about how far off are the weights of the maternal bears?

 

 

 

1. b) What age of the female would seem to be the best for reproduction success? In a few sentences, justify your answer by appealing to the information provided above.

 

 

 

 

 

 

 

 

 

 

 

 

4. Assessing the goodness of fit of a regression line involves considering several things, and no single characteristic of data is sufficient for a good assessment. Consider the characteristics below.  How does each contribute to an assessment of fit?  That is, for each piece of information, what characteristic would indicate a “good” best-fit line?

 

1. a) The shape of the residual plot

 

 

 

 

 

 

 

 

 

1. b) The correlation coefficient

 

 

 

 

 

 

 

 

 

1. c) The demonstration of seriously influential points

 

 

 

 

 

 

 

 

 

1. d) The coefficient of determination