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Exercises 39 and 40 refer to the following setting. We used CensusAtSchool鈥檚 Random Data Selector to choose a sample of 50 Canadian students who completed a survey in 2007鈥�2008. Lefties (1.1) Students were asked, 鈥淎re you right-handed, left-handed, or ambidextrous?鈥� The responses are shown below (R = right-handed; L = left- handed; A = ambidextrous). \(\begin{array}{llllllllllllll}{\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{L}} & {\mathrm{R}} & {\mathrm{R}} \\ {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{A}} \\\ {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{A}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{L}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{L}} & {\mathrm{A}} \\ {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}} & {\mathrm{R}}\end{array}\) (a) Make an appropriate graph to display these data. (b) Over 10,000 Canadian high school students took the CensusAtSchool survey in 2007鈥�2008. What percent of this population would you estimate is left- handed? Justify your answer.

Step by step solution

01

Count the Student Responses

First, count the number of responses for each category (Right-handed, Left-handed, Ambidextrous) from the given data. We find 43 students are right-handed (R), 4 are left-handed (L), and 3 are ambidextrous (A).

02

Calculate Percentages for the Graph

Next, calculate the percentage of each category of handedness based on the total number of students (50). Right-handed: \( \frac{43}{50} \times 100\% = 86\% \), Left-handed: \( \frac{4}{50} \times 100\% = 8\% \), Ambidextrous: \( \frac{3}{50} \times 100\% = 6\% \).

03

Create a Bar Graph

Create a bar graph or a pie chart to visually represent the percentages calculated in Step 2. Each bar or segment should represent one of the three categories: Right-handed (86%), Left-handed (8%), and Ambidextrous (6%). Label each section accordingly.

04

Estimate Population Percentage of Lefties

To estimate the percentage of left-handed students in the larger population of 10,000, use the sample percentage as an estimate. Thus, assume around 8% of the broader student population is left-handed.

05

Justification of Population Estimate

Since we are using a sample random data selection, it represents a good estimate for the entire population. We assume similar trends exist among the larger group, justifying our 8% estimate.

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Key Concepts

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

Data Analysis

Data analysis is a critical component of statistics education. It involves processing and inspecting data to discover useful information. In our exercise, we had data about the handedness of 50 Canadian students, who were either right-handed, left-handed, or ambidextrous.

We started by counting how many students fell into each category. This gave us a clear view of the distribution of responses:

• 43 students were right-handed
• 4 students were left-handed
• 3 students were ambidextrous

Once we had this data, the next step was to calculate the percentages. These percentages help us understand the proportions of the responses, which is a key aspect of data analysis. The calculations showed that 86% were right-handed, 8% were left-handed, and 6% were ambidextrous.

Through data analysis, we can transform raw data into meaningful insights, allowing us to make informed estimates about broader populations. In this case, understanding the handedness of the students helps us predict trends in larger groups.

Sampling Methods

Sampling methods are techniques used to select a group of subjects for study from a larger population. Our exercise used a sample of 50 students from over 10,000 Canadian high school students.

In statistics, using a random sample selection like this is key to getting accurate results. A random sample means every individual had an equal chance of being chosen, which minimizes biases.

The advantage of using a sample rather than surveying the entire population is efficiency. It allows us to make predictions about a population based on a smaller, more manageable group. For instance, even with only 4 left-handed students in a sample of 50, we estimated approximately 8% of the broader population might be left-handed.

This method allows educators and statisticians to draw conclusions about large populations with fewer resources, making it an essential part of statistics education.

Graphical Representation

Graphical representation is the visual depiction of data. It's an effective way to communicate patterns or trends. In this exercise, the bar graph was a chosen method to illustrate the handedness of the sampled students.

With a bar graph, each bar represents a category, such as right-handed, left-handed, or ambidextrous students. The height of each bar reflects the percentage or number of responses in that category.

• Description: Visualize the 86% of right-handed students with one tall bar
• Depiction: Show 8% left-handed with a shorter bar
• Illustration: Include a bar for the 6% ambidextrous students

Graphs are favored for their ability to simplify complex data, making it accessible at a glance. A well-drawn graph helps in quickly understanding the distribution and can aid in discussions or reports.

Using graphical representations enhances the interpretation of statistical data, making it a crucial part of learning and applying statistics concepts.