1. Intro to Stats and Collecting Data
Intro to Stats
3:59 minutesProblem 1.1.40
Textbook Question
In Exercises 37–44, answer the given questions, which are related to percentages.
Texting While Driving USA Today reported results from an Arity survey in which 2018 drivers were asked if they text while driving.
a. Among the respondents, 42% said that they text while driving. What is the exact value that is 42% of the number of respondents?
b. Could the result from part (a) be the actual number of respondents who said that they text while driving? Why or why not?
Verified step by step guidance1
To find the exact value that is 42% of the number of respondents, start by identifying the total number of respondents, which is 2018.
Calculate 42% of 2018 by using the formula: \( \text{Percentage value} = \frac{42}{100} \times 2018 \). This will give you the number of respondents who said they text while driving.
For part (b), consider whether the result from part (a) can be the actual number of respondents. Since the number of respondents must be a whole number, check if the calculated percentage value is an integer.
If the calculated percentage value is not an integer, explain why it cannot be the actual number of respondents. Discuss the concept of rounding and how survey results are typically reported as whole numbers.
Conclude by discussing the implications of rounding in survey data and how it affects the interpretation of results, ensuring clarity on why exact percentages may not always translate to exact whole numbers in practice.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Percentage Calculation
Percentage calculation involves determining a portion of a whole expressed as a fraction of 100. In this context, to find 42% of the 2018 respondents, you multiply 2018 by 0.42. This calculation is essential for quantifying how many drivers admitted to texting while driving based on the survey results.
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Sample Size and Representativeness
Sample size refers to the number of individuals surveyed, which in this case is 2018 drivers. A larger sample size generally provides more reliable results, but it is also crucial that the sample is representative of the broader population. This ensures that the findings can be generalized to all drivers, not just those surveyed.
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Statistical Inference
Statistical inference involves drawing conclusions about a population based on sample data. In part (b) of the question, one must consider whether the calculated number of respondents who text while driving (from part a) accurately reflects the true behavior of all drivers. Factors such as response bias or the survey's methodology can affect the validity of these inferences.
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