Margin of Error and Interpreting Confidence Intervals
A health group study recommends that the total weight of a male student's backpack should not be more than 15% of his body weight. The following is a random sample of male students, recording their body weight and backpack weight (in pounds).
1. Calculate backpack weight as a percentage of body weight by typing [b]=b2/a2[/b] in cell C2, pressing [b]return[/b], then dragging the formula to cell C11.[br]2. Calculate the mean and standard deviation of these percentages. (Use [b]one variable analysis[/b] [icon]/images/ggb/toolbar/mode_onevarstats.png[/icon] and show statistics[img]data:image/png;base64,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[/img]).
mean is 0.188
3. Find the margin of error for the mean you calculated. To do this, use the formula [math]M=2\left(\frac{s}{\sqrt{n}}\right)[/math].
4. What do the results of this study say about backpack weights?
We could be relatively confident in saying that the average backpack percentage is 18.8±1.02%, or between 17.8 and 19.8 percent of body weight, which is over the recommendation.
These problems involve population [b]proportions.[/b] To do this, use the formula:[br][math]M=2\sqrt{\left(\frac{p\left(1-p\right)}{n}\right)}[/math][br]
MOE-Proportion
1. The school newspaper at a large high school reported that 120 out of 200 randomly selected students favor assigned parking spaces. Compute the margin of error. Interpret the resulting interval in context.
1. 0.069, so the proportion of student who favor assigned parking spaces is between 0.531 and 0.669[br]
2. A newspaper in a large city asked 500 women the following: “Do you use organic food products (such as milk, meats, vegetables, etc.)?” 280 women answered “yes.” Compute the margin of error. Interpret the resulting interval in context.
2. The M=0.044, so the proportion of women who use organic foods is between 0.516 and 0.604