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Chapter 5: Problem 18

The same issue of The Chronicle for Higher Education referenced in Exercise 5.17 also reported the following information for degrees awarded to Hispanic students by U.S. colleges in the \(2008-2009\) academic year: A total of 274,515 degrees were awarded to Hispanic students. \- 97,921 of these degrees were Associate degrees. \- 129,526 of these degrees were Bachelor's degrees. \- The remaining degrees were either graduate or professional degrees. What is the probability that a randomly selected Hispanic student who received a degree in \(2008-2009\) a. received an associate degree? b. received a graduate or professional degree? c. did not receive a bachelor's degree?

Short Answer

Expert verified
The probability that a randomly selected Hispanic student who received a degree in 2008-2009: a. received an associate degree is \(\frac{97,921}{274,515}\). b. received a graduate or professional degree is \(\frac{274,515 - (97,921 + 129,526)}{274,515}\). c. did not receive a bachelor's degree is \(\frac{274,515 - 129,526}{274,515}\).

Step by step solution

01

Determine the total number of degrees

The total number of degrees awarded to Hispanic students in the 2008-2009 academic year is 274,515.
02

Calculation for part (a)

Part (a) is asking for the probability that a randomly selected Hispanic student received an associate degree. This can be found by dividing the number of associate degrees awarded (97,921) by the total number of degrees awarded (274,515). Using this, the calculation becomes \(P(Associate Degree) = \frac{97,921}{274,515}\).
03

Calculation for part (b)

For part (b), the question asks for the probability that a randomly selected Hispanic student received a graduate or professional degree. This is found by subtracting the number of associate and bachelor's degrees from the total number of degrees, since the question states that the remaining degrees were either graduate or professional. The calculation becomes \(P(Graduate or Professional Degree) = \frac{274,515 - (97,921 + 129,526)}{274,515}\).
04

Calculation for part (c)

Finally, part (c) asks for the probability that a randomly selected Hispanic student did not receive a bachelor's degree. This probability is found by subtracting the number of bachelor's degrees from the total number of degrees. The calculation comes to \(P(No Bachelor's Degree) = \frac{274,515 - 129,526}{274,515}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Statistics in Education
Understanding statistics in education provides valuable insights into various educational outcomes, including degree completion rates among demographic groups. To compute probabilities using educational data, we begin with accurate collection and categorization of data. In our exercise, we analyzed the number of degrees awarded to Hispanic students in a particular academic year. This exercise in probability calculation is an application of descriptive statistics, a branch of statistics dealing with the analysis of data that provides a description of a sample.

Through educational statistics, stakeholders can make informed decisions based on patterns and trends. For example, when assessing the impact of different programs aimed at supporting Hispanic student success, statisticians would analyze data to determine their effectiveness. This helps schools and policymakers tailor educational strategies to meet the needs of various student populations.
Hispanic Student Degrees
Taking a specific look at the degrees awarded to Hispanic students, we can assess educational attainment within this demographic. By breaking down the types of degrees received—Associate, Bachelor's, and graduate or professional degrees—we can evaluate the educational landscape for Hispanic students. For instance, we can explore the accessibility and attractiveness of higher education among Hispanic students by examining the trends in degree attainment.

Taking the data from our exercise, there's a clear interest and achievement in both Associate and Bachelor's degrees among Hispanic students in the 2008-2009 academic year. Such analysis is crucial for universities and colleges in crafting programs and resources to further support Hispanic students to not only enter higher education but to successfully graduate with degrees that meet their personal and career objectives.
Academic Year Degree Analysis
In the context of our exercise, an academic year degree analysis refers to the study of all degrees conferred over an academic year. By assessing the probabilities of receiving different degrees, educational institutions can monitor students' progression and success rates. This year-over-year analysis can also reveal trends, such as shifts towards certain disciplines or changes in the popularity of graduate studies.

Such a comprehensive review guides schools in understanding trends and needs to possibly reassess their academic offerings. Forecasting future demand for programs and aligning resources to meet that demand is critical for ensuring that institutions remain responsive and relevant to student aspirations and societal needs. The probability calculations we conducted are part of this larger analytical process, underlining the importance of statistics in effectively managing and advancing educational programs.

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Most popular questions from this chapter

A single-elimination tournament with four players is to be held. A total of three games will be played. In Game 1 , the players seeded (rated) first and fourth play. In Game 2 , the players seeded second and third play. In Game \(3,\) the winners of Games 1 and 2 play, with the winner of Game 3 declared the tournament winner. Suppose that the following probabilities are known: \(P(\) Seed 1 defeats Seed 4\()=0.8\) \(P(\) Seed 1 defeats \(\operatorname{Seed} 2)=0.6\) \(P(\) Seed 1 defeats \(\operatorname{Seed} 3)=0.7\) \(P(\) Seed 2 defeats \(\operatorname{Seed} 3)=0.6\) \(P(\) Seed 2 defeats Seed 4\()=0.7\) \(P(\) Seed 3 defeats Seed 4) \(=0.6\) a. How would you use random digits to simulate Game 1 of this tournament? b. How would you use random digits to simulate Game 2 of this tournament? c. How would you use random digits to simulate the third game in the tournament? (This will depend on the outcomes of Games 1 and \(2 .\) ) d. Simulate one complete tournament, giving an explanation for each step in the process. e. Simulate 10 tournaments, and use the resulting information to estimate the probability that the first seed wins the tournament. f. Ask four classmates for their simulation results. Along with your own results, this should give you information on 50 simulated tournaments. Use this information to estimate the probability that the first seed wins the tournament. g. Why do the estimated probabilities from Parts (e) and (f) differ? Which do you think is a better estimate of the actual probability? Explain.

Each time a class meets, the professor selects one student at random to explain the solution to a homework problem. There are 40 students in the class, and no one ever misses class. Luke is one of these students. What is the probability that Luke is selected both of the next two times that the class meets? (Hint: See Example 5.8 )

The authors of the paper "Do Physicians Know when Their Diagnoses Are Correct?" (Journal of General Internal Medicine [2005]: \(334-339\) ) presented detailed case studies to students and faculty at medical schools. Each participant was asked to provide a diagnosis in the case and also to indicate whether his or her confidence in the correctness of the diagnosis was high or low. Define the events \(C, I,\) and \(H\) as follows: \(C=\) event that diagnosis is correct \(I=\) event that diagnosis is incorrect \(H=\) event that confidence in the correctness of the diagnosis is high a. Data appearing in the paper were used to estimate the following probabilities for medical students: $$\begin{aligned} P(C) &=0.261 & & P(I)=0.739 \\ P(H \mid C) &=0.375 & & P(H \mid I)=0.073 \end{aligned} $$Use the given probabilities to construct a "hypothetical 1000 " table with rows corresponding to whether the diagnosis was correct or incorrect and columns corresponding to whether confidence was high or low. b. Use the table to calculate the probability of a correct diagnosis, given that the student's confidence level in the correctness of the diagnosis is high. c. Data from the paper were also used to estimate the following probabilities for medical school faculty: $$\begin{array}{cl} P(C)=0.495 & P(I)=0.505 \\ P(H \mid C)=0.537 & P(H \mid I)=0.252 \end{array}$$ Construct a "hypothetical \(1000 "\) ' table for medical school faculty and use it to calculate the probability of a correct diagnosis given that the faculty member's confidence level in the correctness of the diagnosis is high. How does the value of this probability compare to the value for students calculated in Part (b)?

The Australian newspaper The Mercury (May 30,1995\()\) reported that based on a survey of 600 reformed and current smokers, \(11.3 \%\) of those who had attempted to quit smoking in the previous 2 years had used a nicotine aid (such as a nicotine patch). It also reported that \(62 \%\) of those who had quit smoking without a nicotine aid began smoking again within 2 weeks and \(60 \%\) of those who had used a nicotine aid began smoking again within 2 weeks. If a smoker who is trying to quit smoking is selected at random, are the events selected smoker who is trying to quit uses a nicotine aid and selected smoker who has attempted to quit begins smoking again within 2 weeks independent or dependent events? Justify your answer using the given information.

A large cable company reports that \(42 \%\) of its customers subscribe to its Internet service, \(32 \%\) subscribe to its phone service, and \(51 \%\) subscribe to its Internet service or its phone service (or both). a. Use the given probability information to set up a "hypothetical \(1000 "\) table. b. Use the table to find the following: i. the probability that a randomly selected customer subscribes to both the Internet service and the phone service. ii. the probability that a randomly selected customer subscribes to exactly one of the two services.
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