In Exercises 21-28, find the probability and answer the questions.


Social Networking In a Pew Research Center survey of Internet users, 3732 respondents say that they use social networking sites and 1380 respondents say that they do not use social networking sites. What is the probability that a randomly selected person uses a social networking site? Does that result suggest that it is likely (with a probability of 0.5 or greater) for someone to use social networking sites?

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the probability that a randomly selected person uses social networking sites. Probability is calculated as the ratio of favorable outcomes to the total number of outcomes.
2. Step 2: Identify the given data. The number of respondents who use social networking sites is 3732, and the number of respondents who do not use social networking sites is 1380. The total number of respondents is the sum of these two values.
3. Step 3: Calculate the total number of respondents. Use the formula: $\mathrm{Total}=3732+1380$. This gives the total population surveyed.
4. Step 4: Calculate the probability of using social networking sites. Use the formula: $P\left(\mathrm{Social}\right)=\frac{3732}{\mathrm{Total}}$. Substitute the total value calculated in Step 3.
5. Step 5: Compare the calculated probability to 0.5. If the probability is greater than or equal to 0.5, it suggests that it is likely for someone to use social networking sites. Otherwise, it is unlikely.

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it quantifies the chance that a randomly selected individual from a population uses social networking sites. The formula for calculating probability is the number of favorable outcomes divided by the total number of possible outcomes.

Sample Size

Sample size refers to the number of observations or respondents included in a survey or study. In this case, the total sample size is the sum of those who use social networking sites and those who do not, which is 5112 respondents. A larger sample size generally leads to more reliable and valid results, as it better represents the population being studied.

Statistical Significance

Statistical significance indicates whether the results of a study are likely due to chance or if they reflect a true effect in the population. In this question, determining if the probability of using social networking sites is 0.5 or greater helps assess whether it is likely for a randomly selected person to use these sites. A probability of 0.5 or higher suggests a significant tendency towards using social networking.