Question

are 30,000 adults living in grand city. in examining attitudes toward the news, a research group asked a random sample of grand city adults, what is main source of news? the results are shown below.
main source of news | number of adults
--- | ---
newspapers | 93
internet | 83
television | 125
radio | 108
other | 41
do on the sample, predict the number of adults in grand city whose main source of news is the radio. round your answer to the nearest whole number. und any intermediate calculations.

Explanation:

Step1: Calculate total sample size

First, we find the total number of adults in the sample by adding up the number of adults for each news source.
The number of adults for each source: Newspapers = 93, Internet = 83, Television = 125, Radio = 108, Other = 41.
Total sample size \( n = 93 + 83 + 125 + 108 + 41 \)
\( n = 93+83 = 176 \); \( 176 + 125 = 301 \); \( 301 + 108 = 409 \); \( 409 + 41 = 450 \)

Step2: Find the proportion of radio users in the sample

The number of adults who use radio as the main news source is 108. The proportion \( p \) of radio users in the sample is \( p=\frac{108}{450} \)

Step3: Predict the number of radio users in the population

The total number of adults in Grand City is 30,000. We predict the number of radio users by multiplying the proportion \( p \) by the population size.
Number of radio users \( = 30000\times\frac{108}{450} \)
Simplify \( \frac{108}{450}=\frac{108\div 18}{450\div 18}=\frac{6}{25} \)
Then \( 30000\times\frac{6}{25}=\frac{30000\times6}{25}= 7200 \)

Answer:

7200