Ch 2 Homework
A national survey asked people, "How often do you eat out for dinner, instead of at home?" The frequencies were as follows. Complete parts (a) through (g). (a) Construct a relative frequency distribution of the data. (b) What percentage of respondents answered "Always"? (c) What percentage of respondents answered "Never" or "Rarely"? (d) Construct a frequency bar graph. Choose the correct answer below. (e) Construct a relative frequency bar graph. Choose the correct answer below. (f) Construct a pie chart. Choose the correct answer below. (g) Suppose a person claims that, "2.8% of all people in the nation always eat out." Is this a descriptive or inferential statement?
(a) never - 0.119 rarely - 0.165 sometimes - 0.47 most of the time - 0.218 always - 0.028 (b) 2.8% (c) 28.4% (d) Graph C (e) Graph C (f) Pie Chart A (g) inferential
The data below represent the per capita (average) disposable income (income after taxes) for 25 randomly selected cities in a recent year. Complete parts (a) through (j). (a) Construct a frequency distribution with the first class having a lower class limit of 30,000 and a class width of 6000. (b) Construct a relative frequency distribution with the first class having a lower class limit of 30,000 and a class width of 6000. (c) Construct a frequency histogram of the data. Choose the correct graph below. (d) Construct a relative frequency histogram of the data. Choose the correct graph below. (e) Describe the shape of the distribution. Choose the correct answer below. (f) Construct a frequency distribution with the first class having a lower class limit of 30,000 and a class width of 3000. (g) Construct a relative frequency distribution with the first class having a lower class limit of 30,000 and a class width of 3000. (h) Construct a frequency histogram of the data. Choose the correct graph below. (i) Construct a relative frequency histogram of the data. Choose the correct graph below. (j) Describe the shape of the distribution. Choose the correct answer below.
(a) 30,000-35,999: 14 36,000-41,999: 10 42,000-47,999: 0 48,000-53,999: 1 (b) 30,000-35,999: 0.56 36,000-41,999: 0.4 42,000-47,999: 0 48,000-53,999: 0.04 (c) Graph A (d) Graph B (e) Skewed right (f) 30,000-32,999: 4 33,000-35,999: 10 36,000-38,999: 6 39,000-41,999: 4 42,000-44,999: 0 45,000-47,999: 0 48,000-50,999: 0 51,000-53,999: 1 (g) 30,000-32,999: 0.16 33,000-35,999: 0.4 36,000-38,999: 0.24 39,000-41,999: 0.16 42,000-44,999: 0 45,000-47,999: 0 48,000-50,999: 0 51,000-53,999: 0.04 (h) Graph B (i) Graph C (j) Skewed right
On the basis of a population survey, there were 89.6 million males and 100.0 million females 25 years old or older in a certain country. The educational attainment of the males and females is shown in the accompanying table. Complete parts (a) through (d) below. (a) Construct a relative frequency distribution for males. Express each relative frequency as a decimal. (b) Construct a relative frequency distribution for females. Express each relative frequency as a decimal. (c) Construct a side-by-side relative frequency bar graph, with male numbers represented by the left bars and female numbers represented by the right bars in each category. Choose the correct graph below. (d) Compare each gender's educational attainment. Choose the correct answer below.
(a) A - 0.1217 B - 0.3304 C - 0.1864 D - 0.0748 E - 0.1875 F - 0.0993 (b) A - 0.129 B - 0.312 C - 0.183 D - 0.092 E - 0.187 F - 0.097 (c) Graph D (d) Each gender's educational attainment is about the same.
The data to the right represent the number of people from a certain county, aged 5 to 64, who visited an optometrist over the course of last year. (a) Create a relative frequency distribution. (Round to three decimal places as needed.) (b) Create a frequency histogram. Choose the correct answer below. (c) Create a relative frequency histogram. Choose the correct answer below. (d) What percentage of patients were between 35 and 49? (e) What percentage of patients were 34 or younger?
(a) age 5-19: 0.092 age 20-34: 0.166 age 35-49: 0.343 age 50-64: 0.398 (b) Graph A (c) Graph B (d) 34.3% (e) 25.8%
An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The frequency histogram to the right gives the results. Use the histogram to complete parts (a) through (f). (a) What was the most frequent outcome of the experiment? (b) What was the least frequent? (c) How many times did we observe a 7? (d) How many more 5's were observed than 11's? (e) Determine the percentage of time a 7 was observed. (f) Describe the shape of the distribution. Choose the correct answer below.
(a) 5 (b) 2 (c) 13 (d) 14 (e) 13% (f) skewed right
The accompanying relative frequency ogive represents the composite score on a standardized test for a high school graduating class. Complete parts (a) through (d) below. (a) The percentage of students who had a composite score of 24 or below is about ______. (b) The percentage of students who had a composite score of 28 or above is about ______. (c) If 1,300,699 students from the class took the exam, approximately how many students had a score of 24 or below? 28 or above? Approximately _____ students had a score of 24 or below. Approximately ______ students had a score of28 or above. (d) What is the approximate score at which half the students scored better and half scored worse? The approximate score at which half the students scored better and half scored worse is
(a) 74% (b) 7% (c) 962,517; 91,048 (d) 20
The following data represent the ages of award winners for best actor and best actress in a leading role for the 20 years from 1985 to 2004. Answer parts (a)−(b) below. (a) Construct an ordered back to back stem-and-leaf display. (b) Compare the two populations. What can you conclude from the back to back stem-and-leaf display?
(a) Chart the numbers (b) While most men and most women receive an award in their thirties, women tend to receive the award at a younger age on average than men do.
The accompanying data represent health care expenditures per capita (per person) as a percentage of the gross domestic product (GDP) of a country from 2009 to 2015. Gross domestic product is the total value of all goods and services created during the course of the year. Complete parts (a) through (c) below. (a) Construct a time-series plot that a politician would create to support the position that health care expenditures are increasing and must be slowed. Choose the correct graph below.
(a) Graph C (b) Graph D (c) The scales used in the graph can significantly affect the message. Also, the variable used to convey the message on the graph can make a large difference as well.
An Internet media and market research firm measured the amount of time an individual spends viewing a specific Webpage. The data in the accompanying table represent the amount of time, in seconds, a random sample of 40 surfers spent viewing a Webpage. Create the graphical summary. Write a sentence that describes the data. (a) Create the graphical summary. Choose the correct graph below. (b) Write a sentence that describes the data. Choose the correct answer below.
(a) Graph C (b) The distribution is skewed right
The accompanying data represent the percentage of recent high school graduates (graduated within 12 months before the given year-end) who enrolled in college in the fall. Construct a time-series plot and comment on any trends. (a) Choose the correct time-series plot below. (b) Comment on any trends. Choose the correct comment below.
(a) Graph C (b) The percentage of high school graduates who enrolled in college has generally increased, though there have been some down years.
(a) How is the graph misleading? (b) What could be done to improve the graphic?
(a) It looks like twice as much money is spent on wages than products. (b) The graphs of the bars could be proportional to the percentages.
The data to the right represent the number of customers waiting for a table at 6:00 P.M. for 40 consecutive Saturdays at Bobak's Restaurant. Complete parts (a) through (h) below. (a) Are these data discrete or continuous? Explain. (b) Construct a frequency distribution of the data. (c) Construct a relative frequency distribution of the data. (d) What percentage of the Saturdays had 4 or more customers waiting for a table at 6:00 P.M.? (e) What percentage of the Saturdays had 9 or fewer customers waiting for a table at 6:00 P.M.? (f) Construct a frequency histogram of the data. Choose the correct histogram below. (g) Construct a relative frequency histogram of the data. Choose the correct histogram below. (h) Describe the shape of the distribution. Choose the correct answer below.
(a) The data are discrete because there are a finite or countable number of values. (b) 1-3: 2 4-6: 9 7-9: 16 10-12: 12 13-15: 1 (c) 1-3: 0.05 4-6: 0.225 7-9: 0.4 10-12: 0.3 13-15: 0.025 (d) 95% (e) 67.5% (f) Graph D (g) Graph A (h) The distribution is symmetric because the left and right sides are approximately mirror images.
The pie chart below depicts the beverage size customers choose while at a fast food restaurant. Complete parts (a) through (c). (a) What is the most popular size? What percentage of customers choose this size? (b) What is the least popular size? What percentage of customers choose this size? (c) What percent of customers choose a medium-sized beverage?
(a) XL; 56% (b) Small; 9% (c) 20%
The data in the accompanying table represent the land area and highest elevation for each of seven states of a country. Complete parts (a) and (b). (a) Would it make sense to draw a pie chart for land area? If it makes sense, draw a pie chart. Choose the correct answer below. (b) Would it make sense to draw a pie chart for the highest elevation?
(a) Yes Pie Chart C (b) No
Determine the original set of data. Legend: 1|0 represents 10
10, 11, 17, 21, 24, 24, 27, 28, 33, 35, 35, 35, 37, 38, 40, 41.
Determine the original set of data. (part 2) Legend: 1|0 represents 10
10, 11, 18, 21, 24, 24, 27, 28, 33, 35, 35, 35, 37, 38, 40, 41
Determine whether the following statement is true or false. The shape of the distribution shown is best classified as skewed left.
False
A frequency distribution lists the ______ of occurrences of each category of data, while a relative frequency distribution lists the _____ of occurrences of each category of data.
number; proportion