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Chapter 1: Problem 7

A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program. EPR 616, Research in Child Development EPR 630, Educational Research Planning and Interpretation EPR 631, Nonparametric Statistics EPR 632, Methods of Multivariate Analysis EPR 645, Theory of Measurement EPR 649, Fieldwork Methods in Educational Research EPR \(650,\) Interpretive Methods in Educational Research (a) List all possible two-course selections. (b) Comment on the likelihood that the pair of courses EPR 630 and EPR 645 will be selected.

Short Answer

Expert verified
All possible pairs: 21. Probability of selecting EPR 630 and EPR 645: \( \frac{1}{21} \).

Step by step solution

01

Identify the Courses

List all available courses: EPR 616, EPR 630, EPR 631, EPR 632, EPR 645, EPR 649, EPR 650.
02

Determine Total Pairs

Use the combinations formula to calculate the total number of ways to select 2 courses out of 7. The formula is \(\binom{n}{k}\), where \(n\) is the total number of courses, and \(k\) is the number of courses to select: \(\binom{7}{2} = \frac{7!}{2!(7-2)!} = 21\).
03

List All Possible Combinations

List all combinations of two courses from the provided courses: 1. EPR 616 and EPR 6302. EPR 616 and EPR 6313. EPR 616 and EPR 6324. EPR 616 and EPR 6455. EPR 616 and EPR 6496. EPR 616 and EPR 6507. EPR 630 and EPR 6318. EPR 630 and EPR 6329. EPR 630 and EPR 64510. EPR 630 and EPR 64911. EPR 630 and EPR 65012. EPR 631 and EPR 63213. EPR 631 and EPR 64514. EPR 631 and EPR 64915. EPR 631 and EPR 65016. EPR 632 and EPR 64517. EPR 632 and EPR 64918. EPR 632 and EPR 65019. EPR 645 and EPR 64920. EPR 645 and EPR 65021. EPR 649 and EPR 650
04

Determine Likelihood of Specific Pair

Calculate the likelihood that the pair EPR 630 and EPR 645 will be selected. Since all pairs are equally possible and there are 21 pairs, the likelihood is \( \frac{1}{21} \).

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Key Concepts

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

combinatorial mathematics
Combinatorial mathematics helps us understand how to count combinations. In this exercise, we used it to find the number of possible combinations of two courses out of seven. The formula for combinations is given by: \(\binom{n}{k} = \frac{n!}{k!(n - k)!} \). This formula tells us how many ways we can choose k items from n items without considering the order. For instance, in our exercise, n = 7 (total courses) and k = 2 (courses selected), so we calculate: \[\binom{7}{2} = \frac{7!}{2!(7-2)!} = 21 \]. This means there are 21 ways to select two courses out of seven, each combination being unique.
probability
Probability is the measure of how likely an event is to occur. We used probability to find out how likely it is for a specific pair of courses, like EPR 630 and EPR 645, to be selected from the list. Since we already know there are 21 possible combinations, and each combination is equally likely to be chosen, the probability of selecting any specific pair, including EPR 630 and EPR 645, is: \(\frac{1}{21} \). This fraction means there's a one in 21 chance of selecting that pair if the selection is made randomly. Understanding this concept helps students appreciate how often certain outcomes can occur.
doctoral education
In the context of doctoral education, students must make critical decisions about their course selections. Particularly in a program like educational psychology, selecting courses helps shape their academic and professional future. Choosing the right courses can lead to a strong foundation for their research interests and career goals. For instance, courses like EPR 616 and EPR 645 might provide a student with comprehensive research skills. Doctoral programs often encourage students to balance their courses between required subjects and those that align with their specific research interests. Making informed choices is key to success in a doctoral journey.

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Most popular questions from this chapter

The survey has bias. (a) Determine the type of bias. (b) Suggest a remedy. The village of Oak Lawn wishes to conduct a study regarding the income level of households within the village. The village manager selects 10 homes in the southwest corner of the village and sends an interviewer to the homes to determine household income.

The survey has bias. (a) Determine the type of bias. (b) Suggest a remedy. A polling organization conducts a study to estimate the percentage of households that speaks a foreign language as the primary language. It mails a questionnaire to 1023 randomly selected households throughout the United States and asks the head of household if a foreign language is the primary language spoken in the home. Of the 1023 households selected, 12 responded.

The following abstract appears in The New England Journal of Medicine: BACKGROUND. The relation between passive smoking and lung cancer is of great public health importance. Some previous studies have suggested that exposure to environmental tobacco smoke in the household can cause lung cancer, but others have found no effect. Smoking by the spouse has been the most commonly used measure of this exposure. METHODS. In order to determine whether lung cancer is associated with exposure to tobacco smoke within the household, we conducted a case-control study of 191 patients with lung cancer who had never smoked and an equal number of persons without lung cancer who had never smoked. Lifetime residential histories including information on exposure to environmental tobacco smoke were compiled and analyzed. Exposure was measured in terms of "smokeryears," determined by multiplying the number of years in each residence by the number of smokers in the household. RESULTS. Household exposure to 25 or more smoker-years during childhood and adolescence doubled the risk of lung cancer. Approximately 15 percent of the control subjects who had never smoked reported this level of exposure. Household exposure of less than 25 smoker-years during childhood and adolescence did not increase the risk of lung cancer. Exposure to a spouse's smoking, which constituted less than one third of total household exposure on average, was not associated with an increase in risk. CONCLUSIONS. The possibility of recall bias and other methodologic problems may influence the results of casecontrol studies of environmental tobacco smoke. Nonetheless, our findings regarding exposure during early life suggest that approximately 17 percent of lung cancers among nonsmokers can be attributed to high levels of exposure to cigarette smoke during childhood and adolescence. (a) What is the research objective? (b) What makes this study a case-control study? Why is this a retrospective study? (c) What is the response variable in the study? Is it qualitative or quantitative? (d) What is the explanatory variable in the study? Is it qualitative or quantitative? (e) Can you identify any lurking variables that may have affected this study? (f) What is the conclusion of the study? Can we conclude that exposure to smoke in the household causes lung cancer? (g) Would it be possible to design an experiment to answer the research question in part (a)? Explain.

The survey has bias. (a) Determine the type of bias. (b) Suggest a remedy. A newspaper article reported, "The Cosmopolitan magazine survey of more than 5000 Australian women aged \(18-34\) found about 42 percent considered themselves overweight or obese."

Define simple random sampling.
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