/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 For each of the following situat... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 14

For each of the following situations, give a set of possible data values that might arise from making the observations described. a. The manufacturer for each of the next 10 automobiles to pass through a given intersection is noted. b. The grade point average for each of the 15 seniors in a statistics class is determined. c. The number of gas pumps in use at each of 20 gas stations at a particular time is determined. d. The actual net weight of each of 12 bags of fertilizer having a labeled weight of \(50 \mathrm{lb}\) is determined.

Short Answer

Expert verified
The data sets for the various situations might be: (a) ['Toyota', 'Nissan', 'Honda', 'BMW', 'Mercedes', 'Ford', 'Toyota', 'Honda', 'BMW', 'Chevrolet'], (b) [4.0, 3.7, 3.8, 3.9, 4.0, 3.7, 3.8, 4.0, 3.6, 3.7, 3.8, 3.9, 3.9, 4.0, 3.7], (c) [5, 2, 6, 4, 5, 1, 3, 7, 8, 4, 2, 4, 5, 7, 6, 8, 5, 4, 3, 2], (d) [50.1, 49.9, 50.0, 50.2, 49.8, 50.0, 50.1, 50.2, 49.9, 50, 50.1, 50.0]

Step by step solution

01

Manufacturer of next 10 autos

From the given scenario, make a note of the car manufacturer for each of the next 10 cars that pass an intersection. The data set might look like this ['Toyota', 'Nissan', 'Honda', 'BMW', 'Mercedes', 'Ford', 'Toyota', 'Honda', 'BMW', 'Chevrolet'].
02

GPAs of 15 seniors

Consider the grade point averages (GPA) of 15 seniors in a statistics class. Be sure to note that GPAs generally range from 0.0 (lowest) to 4.0 (highest). Thus, the data set could be [4.0, 3.7, 3.8, 3.9, 4.0, 3.7, 3.8, 4.0, 3.6, 3.7, 3.8, 3.9, 3.9, 4.0, 3.7].
03

Number of gas pumps in use

Look at how many gas pumps are in use at each of the 20 gas stations. This will differ greatly depending on the time of day and the size of each station. A possible set of data could be [5, 2, 6, 4, 5, 1, 3, 7, 8, 4, 2, 4, 5, 7, 6, 8, 5, 4, 3, 2].
04

Net weight of 12 bags of fertilizer

The bags of fertilizer are labeled '50 lb', but the exact weight may vary slightly. Assuming the variation isn't huge, the data set might look something like this measured in lb: [50.1, 49.9, 50.0, 50.2, 49.8, 50.0, 50.1, 50.2, 49.9, 50, 50.1, 50.0].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Data Collection
Data collection is the process of gathering information to analyze and make decisions. It is critical to ensure that the data collected is precise and pertinent. In our scenarios, we are collecting diverse types of data:
  • For automobiles, we note the manufacturers passing through a specific intersection.
  • For students, we gather their grade point averages.
  • For gas stations, we observe the number of pumps in use.
  • For fertilizer bags, we measure the net weight.
Each of these examples shows different methods of data collection based on the nature of the observation. In practice, clarity in what needs to be recorded and consistency in how it is recorded are crucial.
Data Analysis
Once data is collected, the next step is data analysis. The aim here is to uncover insights and patterns that inform decisions. Data analysis can be as simple or as complex as needed, depending on the problem at hand.
  • For the list of car manufacturers, data analysis might involve determining the most common manufacturers at the intersection.
  • For GPAs, one might calculate the mean or median to determine the class's overall performance.
  • Analyzing the gas pump data could provide insights into busy times or variations in station size.
  • For the weights of fertilizer bags, data analysis may check for consistency in filling processes.
Techniques like averaging, finding medians, and identifying trends are basic yet powerful tools in data analysis.
Distributions
A distribution provides insight into how data points are spread over a range. Understanding distributions is vital in statistics, as it reflects the nature of data. For instance:
  • The distribution of car manufacturers might be uniform or skewed towards a few common brands.
  • For the GPAs, the distribution gives an idea of the academic performance range within the class.
  • The number of pumps in use might show a distribution that reflects certain patterns at different times of the day.
  • Weights of fertilizer bags probably follow a normal distribution if the filling processes are consistent.
Analyzing distributions helps in visualizing data spread and identifying anomalies or trends.
Quantitative Variables
Quantitative variables are numerical and can be measured or counted. In our examples, we have a variety of quantitative variables:
  • GPAs are a continuous quantitative variable ranging between 0.0 to 4.0.
  • The number of gas pumps in use is a discrete quantitative variable as they can only be whole numbers.
  • The net weight of fertilizer bags is another continuous quantitative variable because it can take any value within a given range.
Understanding whether a variable is discrete or continuous helps in choosing the right statistical tools for analysis.

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Most popular questions from this chapter

'Ozzie and Harriet Don't Live Here Anymore" (San Luis Obispo Tribune, February 26,2002 ) is the title of an article that looked at the changing makeup of America's suburbs. The article states that nonfamily households (e.g.' homes headed by a single professional or an elderly widow) now outnumber married couples with children in suburbs of the nation's largest metropolitan areas. The article goes on to state: In the nation's 102 largest metropolitan areas, "nonfamilies" comprised 29 percent of households in 2000 , up from 27 percent in 1990 . While the number of married-with-children homes grew too, the share did not keep pace. It declined from 28 percent to 27 percent. Married couples without children at home live in another 29 percent of suburban households. The remaining 15 percent are single-parent homes. Use the given information on type of household in 2000 to construct a frequency distribution and a bar chart. (Be careful to extract the 2000 percentages from the given information).

For the following numerical attributes, state whether each is discrete or continuous. a. The number of insufficient-funds checks received by a grocery store during a given month b. The amount by which a 1-lb package of ground beef decreases in weight (because of moisture loss) before purchase c. The number of New York Yankees during a given year who will not play for the Yankees the next year d. The number of students in a class of 35 who have purchased a used copy of the textbook

Give a brief definition of the terms population and sample.

The article "Americans Drowsy on the Job and the Road" (Associated Press, March 28, 2001) summarized data from the 2001 Sleep in America poll. Each individual in a sample of 1004 adults was asked questions about his or her sleep habits. The article states that "40 percent of those surveyed say they get sleepy on the job and their work suffers at least a few days each month, while 22 percent said the problems occur a few days each week. And 7 percent say sleepiness on the job is a daily occurrence." Assuming that everyone else reported that sleepiness on the job was not a problem, summarize the given information by constructing a relative frequency bar chart.

The supervisors of a rural county are interested in the proportion of property owners who support the construction of a sewer system. Because it is too costly to contact all 7000 property owners, a survey of 500 owners (selected at random) is undertaken. Describe the population and sample for this problem.
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