Question

ap stats lesson 1.2 homework

1. a research organization in australia was interested in finding out how often school - aged students were skipping breakfast. the results are summarized in the side - by - side bar graphs.

a. estimate the percent of students in grades 4 - 7 that sometimes skip breakfast.
b. estimate the percent of students in grades 8 - 12 that sometimes skip breakfast.
c. do we know for certain that a greater number of students in the survey from grades 8 - 12 sometimes skip breakfast than from grades 4 - 7? explain.
a recent pew research survey investigated the type of community people live in - classified as either urban, suburban, or rural. survey respondents were asked if they would want to move to a different community. the graph shows the results.
a. explain what the 37% in the first segmented bar graph represents.
b. explain what the 25% in the third segmented bar graph represents.
c. there is an association between the type of community a person lives in and their opinion about moving to a different community. explain why.
d. draw an example of what the segmented bar graphs would look like if there were no association.

Explanation:

Step1: Estimate for grades 4 - 7

By looking at the side - by - side bar graph for grades 4 - 7, the relative frequency of students who sometimes skip breakfast appears to be about 0.15.

Step2: Estimate for grades 8 - 12

By looking at the side - by - side bar graph for grades 8 - 12, the relative frequency of students who sometimes skip breakfast appears to be about 0.25.

Step3: Analyze number comparison

We do not know for certain that a greater number of students in grades 8 - 12 sometimes skip breakfast than from grades 4 - 7. The relative frequencies tell us about the proportion within each group, but we do not know the actual number of students in each grade range (4 - 7 and 8 - 12). If the number of students in grades 4 - 7 is much larger than in grades 8 - 12, it is possible that there are more students who sometimes skip breakfast in grades 4 - 7 despite the lower relative frequency.

Step4: Explain 37% in urban graph

The 37% in the first segmented bar graph (urban) represents the percentage of urban residents who would like to move to a different community.

Step5: Explain 25% in rural graph

The 25% in the third segmented bar graph (rural) represents the percentage of rural residents who would like to move to a different community.

Step6: Explain association

There is an association between the type of community a person lives in and their opinion about moving to a different community because the percentages of those who want to move, are not sure, and do not want to move vary across the urban, suburban, and rural categories. For example, 37% of urban residents want to move compared to 34% of suburban and 25% of rural residents.

Step7: Draw no - association example

In a segmented bar graph with no association, the proportion of "Yes", "Not sure", and "No" responses would be the same across the urban, suburban, and rural categories. So, the height of each segment (Yes, Not sure, No) would be the same for all three community types.

Answer:

a. Approximately 15%
b. Approximately 25%
c. No, because we only have relative frequencies and not the actual number of students in each grade - range.
a. It represents the percentage of urban residents who would like to move to a different community.
b. It represents the percentage of rural residents who would like to move to a different community.
c. Because the percentages of those who want to move, are not sure, and do not want to move vary across urban, suburban, and rural categories.
d. The proportion of "Yes", "Not sure", and "No" responses would be the same across urban, suburban, and rural categories in the segmented bar graph.