Statistics Unlocking

Statistics Unlocking the Power of Data, 3e Robin Lock, Patti Frazer Lock, Kari Lock Morgan, Eric Lock, Dennis Lock

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CHAPTER 11

Section 1.1 Solutions 1.1(a) The cases are the people who are asked the question.(b) The variable is whether each person supports the law or not. It is categorical.

1.2(a) The cases are the 100 stocks.(b) The variable is the percentage change, which is a numerical quantity, for each of the stocks. It is quantitative.

1.3(a) The cases are the teenagers in the sample.(b) The variable is the result (yes or no) indicating whether each teenager eats at least five servings a day of fruits and vegetables. It is categorical.

1.4(a) The cases are the bunches of bananas in the sample.(b) The variable is the number of days until the bananas go bad. It is quantitative.

1.5(a) The 10 beams that were tested.(b) The force at which each beam broke. It is quantitative.

1.6(a) The cases are countries of the world.(b) The variable is whether or not the literacy rate is over 75%. It is categorical.

1.7Since we expect the number of years smoking cigarettes to impact lung capacity, we think of the number of years smoking as the explanatory variable and the lung capacity as the response variable.

1.8Since we expect the amount of fertilizer used to impact the yield (and not the other way around), we think of the amount of fertilizer as the explanatory variable and the yield of the crop as the response variable.

1.9Ingesting more alcoholic drinks will cause the level of alcohol in the blood to increase, so the number of drinks is the explanatory variable and blood alcohol content is the response.

1.10The world record time will continue to decrease as the years go by so we expect the year to impact marathon record time. We think of the year as the explanatory variable and the record time as the response variable.

1.11(a)YearandHigherSATare categorical. The other six variables are all quantitative, althoughSiblings might be classified as either categorical or quantitative.(b) There are many possible answers, such as “What proportion of the students are first year students?” or “What is the average weight of these students?” (c) There are many possible answers, such as “Do seniors seem to weigh more than first year students?” or “Do students with high Verbal SAT scores seem to also have high Math SAT scores?” 1.12(a) In addition to the identification column,Country,thereare24variables.WeseethatDeveloped is a categorical variable, while the other 23 variables are all quantitative.(b) There are many possible answers, such as “What is the average life expectancy for all countries of the world?” or “What proportion of countries are developed?” 2 / 4

2CHAPTER 1

(c) There are many possible answers, such as “Do countries with a greater land area have a larger percent rural?” or “Do countries that spend a relatively large amount on the military spend a relatively small amount on health care?” or “Do developed countries have a longer life expectancy than developing countries?” 1.13(a) The explanatory variable is the type of format in which the story is presented. It is categorical, with three categories (audio, illustrated, and animated).(b) The response variable is the measure of brain connectivity. It is quantitative.(c) The cases are the four-year-olds in the study, so there are 27 cases.

1.14(a) The cases are female gamers in Great Britain.(b) There are three variables mentioned: Whether the gamers had received obscene messages (categorical), how many hours a week they played (quantitative), and whether they felt there were enough strong female characters in games (categorical).(c) There are 1151 cases and 3 variables, so the dataset will have 1151 rows and 3 columns.

1.15(a) The cases are the students in the college physics class.(b) There are 3 variables: Whether the student was assigned to an active or passive learning class, the measure of how much the student thought they learned, and the score of actual learning on the test.The class assignment is categorical, while the other two are quantitative.(c) The class assignment (active or passive) is the explanatory variable, while the two measures of learning are response variables.(d) The students in the physics class are the cases, so there are 154 + 142 = 296 cases. There are three variables, so the dataset will have 296 rows and 3 columns.

1.16There are at least two variables. One variable is whether or not the spider engaged in mock-sex. This variable is categorical and the explanatory variable. Another variable is length of time to reach the point of real mating once the spider is fully mature. This variable is quantitative and the response variable.

1.17The individual cases are the lakes from which water samples were taken. For each lake in the sample, we record the concentration of estrogen in the water and the fertility level of fish. Both are quantitative variables.

1.18There are two variables. One variable indicates the presence or absence of the gene variant and the second variable indicates which of the three ethnic groups the individual belongs to. Both variables are categorical.

1.19(a) There are 10 cases, corresponding to the 10 cities. The two variables are population, which is quantitative, and the hemisphere the city is in, which is categorical.(b) We need two columns, one for each variable. The columns can be in either order. See the table. 3 / 4

CHAPTER 13

PopulationHemisphere 37 Eastern 26 Eastern 23 Eastern 22 Eastern 21 Eastern 21 Eastern 21 Eastern 21 Western 20 Western 19 Western 1.20(a) There are 7 cases, representing the seven pigeons. There are two variables. One is the sex of the pigeon, which is categorical, and the other is the speed of the pigeon, which is quantitative.(b) The dataset will have 7 rows and 2 columns. See the table. (The seven cases can be listed in any order.) SexSpeed Hen1676 Hen1452 Hen1449 Cock1458 Cock1435 Cock1418 Cock1413 1.21(a) The cases are the homing pigeons, so there are 1412 of them.(b) There are 4 variables. Two are categorical (loft, sex) and two are quantitative (distance, speed).(c) The dataset will have 1412 rows (one for each pigeon) and 4 columns (one for each variable).

1.22One variable is whether each male was fed a high-fat diet or a normal diet. This is the explanatory variable and it is categorical. The response variable is whether or not the daughters developed metabolic syndrome, which is also categorical.

1.23One variable is whether the young female mice lived in an enriched environment or not. This is the explanatory variable and it is categorical. The response variable is how fast the offspring learned to navigate mazes and is quantitative.

1.24(a) The mode of transportation (e.g., bus, car, walk) gives a categorical value for each student.(b) The answer about allergies (yes or no) gives a categorical value for each student.(c) The proportion of students in the sample who are vegetarians is a single number, based on all of the students, and does not give a value for each individual student. It is not a variable for the dataset.(d) The number of hours worked at a paid job gives a quantitative value for each student.(e) The difference in hours of sleep on school nights and non-school nights gives a quantitative value for each student.(f) The maximum time to get to school is a single number, based on all of the students, and does not give a value for each individual student. It is not a variable for the dataset.

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