Question

The report "Twitter in Higher Education: Usage Habits and Trends of Today's College Faculty" (Magna Publications, September 2009) describes a survey of nearly 2,000 college faculty. The report indicates the following: \- \(30.7 \%\) reported that they use Twitter, and \(69.3 \%\) said that they do not use Twitter. \- Of those who use Twitter, \(39.9 \%\) said they sometimes use Twitter to communicate with students. \- Of those who use Twitter, \(27.5 \%\) said that they sometimes use Twitter as a learning tool in the classroom. Consider the chance experiment that selects one of the study participants at random. a. Two of the percentages given in the problem specify unconditional probabilities, and the other two percentages specify conditional probabilities. Which are conditional probabilities, and how can you tell? b. Suppose the following events are defined: \(T=\) event that selected faculty member uses Twitter \(C=\) event that selected faculty member sometimes uses Twitter to communicate with students \(L=\) event that selected faculty member sometimes uses Twitter as a learning tool in the classroom Use the given information to determine the following probabilities: i. \(P(T)\) iii. \(P(C \mid T)\) ii. \(P\left(T^{C}\right)\) iv. \(P(L \mid T)\) c. Construct a "hypothetical 1000 " table using the given probabilities and use it to calculate \(P(C),\) the probability that the selected study participant sometimes uses Twitter to communicate with students. d. Construct a "hypothetical 1000 " table using the given probabilities and use it to calculate the probability that the selected study participant sometimes uses Twitter as a learning tool in the classroom.

Short answer

The conditional probabilities are the 39.9% and the 27.5% figures. The calculated probabilities are: \(P(T) = 0.307\), \(P(C | T) = 0.399\), \(P(T^{C}) = 0.693\), and \(P(L | T) = 0.275\). The hypothetical 1000 table helps us determine \(P(C) = 0.123\) and \(P(L) = 0.084\).

Step-by-step solution

Identify Unconditional and Conditional Percentages

The unconditional probabilities are those that concern the overall population being studied - \(30.7\%\) and \(69.3\%\), which are the overall percentages of faculty who use or don't use Twitter respectively. Conditional probabilities are the ones that concern a specific condition - \(39.9\%\) and \(27.5\%\). Those are percentages of faculty who use Twitter and also use it for specific purposes (communicating with students or as a learning tool).

Calculate Probabilities

Based on the given percentages:- \(P(T) = 30.7 / 100 = 0.307\) which is the probability of a faculty member using Twitter.- \(P(C | T) = 39.9 / 100 = 0.399\) which represents the probability that a faculty member uses Twitter to communicate with students, given that they use Twitter.- \(P(T^{C}) = 1 - P(T) = 1 - 0.307 = 0.693\) is the probability of a faculty member not using Twitter.- \(P(L | T) = 27.5 / 100 = 0.275\) which is the probability that a faculty member uses Twitter as a learning tool, given that they use Twitter.

Creating the Hypothetical 1000 table

Imagine that there are 1000 faculty members in total. Then we would expect 307 (0.307*1000) to use Twitter. Among these 307 Twitter users: - About 123 (0.399*307) would use Twitter to communicate with students (event C)- Around 84 (0.275*307) would use Twitter as a learning tool (event L)

Calculate P(C) and P(L)

P(C) can be calculated as the number of faculty members who use Twitter to communicate with students divided by the total number of faculty members. Hence, P(C) = 123/1000 = 0.123. Similarly, P(L) = 84/1000 = 0.084.

Key concepts

Unconditional Probability

Understanding unconditional probability is essential when studying statistics, especially in the context of education. Unconditional probability, also known as marginal or prior probability, refers to the likelihood of an event occurring without considering the impact of any other events. In educational settings, such as the survey on Twitter usage among college faculty, unconditional probabilities help educators and researchers identify the general usage patterns without being influenced by specific conditions or subsets.

For instance, in the case study, the unconditional probabilities are identified as the overall percentages of faculty who use or do not use Twitter—30.7% and 69.3%, respectively. These probabilities provide a baseline from which other more specific, conditional probabilities can be understood. Such statistics can guide decision-making in higher education, helping institutions understand general trends among faculty members.

Twitter Usage Among Faculty

In today's digital age, understanding the extent of social media usage, like Twitter, among faculty members in higher education is valuable. Social media platforms can play a significant role in academic communication and classroom engagement.

According to the case study, 30.7% of the surveyed faculty members use Twitter. When delving deeper, the study reveals that among those who use Twitter, some do so to communicate with students or use it as a learning tool in the classroom. This information might influence institutional policies, professional development, and potential guidelines for social media use. It shows how faculty are adapting to new forms of technology and the need for sufficient support and resources for those who choose to integrate these tools into their teaching methods.

Probability Calculation

Probability calculation is a fundamental aspect of statistics that allows us to quantify the likelihood of events. It's critical for students to understand how to calculate both unconditional and conditional probabilities. In the Twitter usage case study, we first calculated the unconditional probabilities of faculty using Twitter, as well as the complement, those not using Twitter. Conditional probabilities were then calculated for specific behaviors given that an individual uses Twitter.

Understanding these calculations aids students in determining the likelihood of events within subsets of a population, which is particularly useful in research and decision-making within educational contexts. This comprehension can lead to more informed discussions around the integration of technology in higher education.

Statistics in Higher Education

Statistics play a significant role in higher education by providing key insights into various aspects of academic life. From analyzing student success rates to evaluating teaching methods, statistical analysis is pivotal. In the context of our Twitter usage study, statistics help map out the landscape of how contemporary tools are being used in education.

This specific case study about Twitter usage offers valuable data that can impact policy-making, resource allocation, and overall strategy in education settings. By assessing these patterns through statistical analysis, educators and administrators can make evidence-based decisions that may enhance learning experiences and pedagogical approaches. It's through statistics that higher education can evolve with technological advances and changing educational trends.