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. the results are shown in the table. a. identify the explanatory variable and the response variable. b. what percent of all adults surveyed are 45 years or older and prefer listening to cds? c. what percent of all adults surveyed prefer listening to the radio? d. of those adults that prefer streaming, what percent are less than 45 years old? 4. 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. 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.

Explanation:

Step1: Identify variables

The explanatory variable is age (Age < 45 or Age 45+), and the response variable is the preferred listening format (Streaming, Radio, Digital File, CDs).

Step2: Calculate total number of surveyed adults

\[386 + 138+124 + 29+306+389+109+95=1586\]

Step3: Answer part b

Number of adults 45 years or older and prefer CDs is 95. Percentage is \(\frac{95}{1586}\times100\approx 6.0\%\)

Step4: Answer part c

Number of adults who prefer radio is \(138 + 389=527\). Percentage is \(\frac{527}{1586}\times 100\approx 33.2\%\)

Step5: Answer part d

Number of adults who prefer streaming is \(386+306 = 692\). Number of those less than 45 years old who prefer streaming is 386. Percentage is \(\frac{386}{692}\times100\approx 55.8\%\)

Step6: Answer 4a

Number of adults less than 45 years old is \(386+138+124 + 29=677\). Number of those who prefer streaming is 386. Percentage is \(\frac{386}{677}\times100\approx 57.0\%\)

Step7: Answer 4b

Number of adults 45 years or older is \(306+389+109+95 = 909\). Number of those who prefer streaming is 306. Percentage is \(\frac{306}{909}\times100\approx 33.7\%\)

Step8: Answer 4c

Yes, there is an association. The percentage of those who prefer streaming is higher among those less than 45 years old (\(57.0\%\)) compared to those 45 years or older (\(33.7\%\)). Also, the preferences for other formats like radio, digital - files and CDs vary by age groups.

Answer:

a. Explanatory variable: Age; Response variable: Preferred listening format
b. Approximately \(6.0\%\)
c. Approximately \(33.2\%\)
d. Approximately \(55.8\%\)
4a. Approximately \(57.0\%\)
4b. Approximately \(33.7\%\)
4c. Yes, there is an association. The percentage of those who prefer streaming is higher among those less than 45 years old compared to those 45 years or older, and preferences for other formats vary by age groups.