Question

1. a cbs news survey asked a random sample of u.s. adults to identify their age and their preferred format for listening to music. a table and segmented bar graph of the results are shown.

age (years)
preferred listening format
streaming
radio
digital files
cds
ages < 45
386
138
124
29
ages 45+
306
389
109
95
a. of the adults in the survey who are less than 45 years old, what percent prefer streaming?
b. of the adults in the survey who are 45 years or older, what percent prefer streaming?
c. is there an association between age and preferred listening format? explain.

1. based on the following graph, a counselor concluded that the number of students enrolled in ap precalculus was more than double the number of students enrolled in ap statistics. do you agree? explain.
2. in the following graph, it appears that toyota has sales that are more than 4 times as big as sales from ford or honda. explain why this is misleading.

Explanation:

Step 1: Calculate total number of adults less than 45

Add up the number of adults in each listening - format category for those less than 45 years old: $386 + 138+124 + 29=677$.

Step 2: Calculate percentage of adults less than 45 who prefer streaming

The number of adults less than 45 who prefer streaming is 386. The percentage is $\frac{386}{677}\times100\%\approx57.0\%$.

Step 3: Calculate total number of adults 45 or older

Add up the number of adults in each listening - format category for those 45 years or older: $306+389 + 109+95 = 909$.

Step 4: Calculate percentage of adults 45 or older who prefer streaming

The number of adults 45 or older who prefer streaming is 306. The percentage is $\frac{306}{909}\times100\%\approx33.7\%$.

Step 5: Analyze association between age and listening format

The percentage of adults less than 45 who prefer streaming ($57.0\%$) is much higher than the percentage of adults 45 or older who prefer streaming ($33.7\%$). Also, looking at other formats, the preferences vary by age. So, there is an association between age and preferred listening format.

Step 6: Analyze AP - enrollment graph

The frequency of students in AP Statistics is around 120, and the frequency of students in AP Pre - calculus is around 170. Since $170<2\times120 = 240$, the number of students enrolled in AP Pre - calculus is not more than double the number of students enrolled in AP Statistics.

Step 7: Analyze automotive sales graph

The graph uses three - dimensional car icons. The height of the Toyota icon is about 4 times the height of the Ford or Honda icons, but the volume of the three - dimensional icons gives a misleading impression. If we consider only the vertical scale (sales in millions), the difference is not as extreme as the three - dimensional representation suggests.

Answer:

a. Approximately $57.0\%$
b. Approximately $33.7\%$
c. Yes, because the percentages of adults who prefer streaming differ significantly between the two age groups, and preferences for other formats also vary by age.

1. No, because the frequency of students in AP Pre - calculus (about 170) is less than double the frequency of students in AP Statistics (about 120).
2. The graph uses three - dimensional icons, and the volume of the icons gives a misleading impression. The actual difference in sales based on the vertical scale is not as extreme as the three - dimensional representation suggests.