In: Statistics and Probability

A school district developed an after-school math tutoring program for high school students. To assess the effectiveness of the program, struggling students were randomly selected into treatment and control groups. A pre-test was given to both groups before the start of the program. A post-test assessing the same skills was given after the end of the program. The study team determined the effectiveness of the program by comparing the average change in pre- and post-test scores between the two groups. During the course of the program, some students in both the treatment and control groups either dropped out of school or they moved away with their families. Could this attrition potentially distort the estimated effectiveness of the tutoring program? Defend your answer.

- attrition likely reduces the statistical power of the analyses of the available data
- attrition may compromise the external validity of the study, especially in those circumstances in which the likelihood of response is related to observed characteristics, such as race or place of residence. In those instances, the resulting parameter estimates may generalize only to a subset of the population of interest

Example, that all African American participants drop out of an evaluation. In that instance, the study's findings likely generalize only to the remaining racial and ethnic groups in the study.

- attrition is often linked to a range of characteristics in a complex manner. As a result, the population to which study findings generalize can be difficult to identify or describe.
- attrition also compromise the internal validity of a study. Particularly problematic are those instances in which the likelihood of response is related to the values of the variable for which values are only partially observed. This sort of attrition seems possible in many cases.

Example, an intervention targeting aggressive adolescents. If individuals who are incarcerated are less likely to participate in follow-up interviews, then aggression likely varies between those who do and do not participate.

**Alternative
ways to handle Attrition**

- Create a project identity.
- Establish meaningful networks.
- Consistently reward participants.
- Develop and maintain a baseline
- Inform participants about the schedule of follow-up interviews

Andy teaches high school math for the Metro School District. In
2018, she has incurred the following expenses associated with her
job:
Noncredit correspondence course on history $ 800 Teaching cases
for classroom use $1,900
Andy’s employer does not provide any funding for the
correspondence course or teaching cases.
Use an available tax service to identify the amount she can
deduct, if any, as a “For AGI” deduction and the amount, if any, as
a “From AGI” deduction.
Prepare a...

In the last decade, only 50.4% of high school students in
Tampa’s school district graduated high school. Aiko believes her
high school in St. Petersburg has a higher graduation rate. She
collects a random sample of 54 former students of her high school
and found that 33 of them graduated. Test Aiko’s belief using a
significance level of 0.05.

(8 pts) The superintendent of a large school district
speculated that high school students involved in extracurricular
activities had a lower mean number of absences per year than high
school students not in extracurricular activities. She generated a
random sample of students from each group and recorded the number
of absences each student had in the most recent school year. The
data are listed below. Test the superintendent’s claim at the α=.01
significance level. [To receive full credit, your response...

The superintendent of a large school district speculated that
high school students involved in extracurricular activities had a
lower mean number of absences per year than high school students
not in extracurricular activities. She generated a random sample of
students from each group and recorded the number of absences each
student had in the most recent school year. The data are listed
below. Test the superintendent’s claim at the α=.01 significance
level. [To receive full credit, your response should be...

(20) 2.A school boasts of its tutoring program offered to
students. Two samples of 71 students each are taken. The first
sample consists of students who have not taken part in the tutoring
program while the second sample consists of students who have taken
part in the tutoring program. An aptitude test was given to both
samples. The first sample showed a mean score of 150 with a
standard deviation of 20 while the second sample showed a mean
score...

A school boasts of its tutoring program offered to students. Two samples of 71 students each are taken. The first sample consists of students who have not taken part in the tutoring program while the second sample consists of students who have taken part in the tutoring program. An aptitude test was given to both samples. The first sample showed a mean score of 150 with a standard deviation of 20 while the second sample showed a mean score of 158 with a standard...

Alice is operating a small nonprofit that provides subsidized
tutoring services to high school students in underserved areas.
Approximately 60% of the direct costs of tutoring are billed to
schools attended by the clients, while approximately 20% are billed
directly to the students. The remainder comes from general
operating funds provided by foundations and individual donations.
Assume that Alice knows the following:
Of the funds billed directly to schools, two-thirds are paid in
the month following the delivery of service,...

Within a school district, students were randomly assigned to
one of two Math teachers - Mrs. Smith and Mrs. Jones. After the
assignment, Mrs. Smith had 30 students, and Mrs. Jones had 25
students. At the end of the year, each class took the same
standardized test. Mrs. Smith's students had an average test score
of 78, with a standard deviation of 10; and Mrs. Jones' students
had an average test score of 85, with a standard deviation of 15....

The Studious Frog provides study support and tutoring services
for high school students during their finals. All services require
cash payment in advance. Studious Frog provides an Finals Prep
course for $480, as well as a Post- Finals Review course for $120.
The finals prep course takes place before the students have their
final tests, and the finals review course takes place after finals
are complete. During December 2022, The Studious Frog offered a
promotional package where students could purchase...

Q1 You operate a small nonprofit that provides subsidized
tutoring services to high school students in underserved areas.
Approximately 60% of the direct costs of tutoring are billed to
schools attended by your clients, while approximately 20% are
billed directly to the students. The remainder comes from general
operating funds provided by foundations and individual donations.
Assume that you know the following:
Of the funds billed directly to schools, two thirds are paid in
the month following delivery of service,...

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