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Chapter 1: Q5E (page 12)

Many universities and colleges have instituted supplemental

instruction (SI) programs, in which a student facilitator meets regularly with a small group of students enrolled in the course to promote discussion of course material and enhance subject mastery. Suppose that students in a large statistics course (what else?) are randomly divided into a control group that will not participate in SI and a treatment group that will participate. At the end of the term, each student鈥檚 total score in the course is determined.

a. Are the scores from the SI group a sample from an existing population? If so, what is it? If not, what is the relevant conceptual population?

b. What do you think is the advantage of randomly dividing the students into the two groups rather than letting each student choose which group to join?

c. Why didn鈥檛 the investigators put all students in the treatment group? [Note:The article 鈥淪upplemental Instruction: An Effective Component of Student Affairs Programming鈥� (J. of College Student Devel., 1997: 577鈥�586) discusses the analysis of data from several SI programs.]

Short Answer

Expert verified

a. No, All the students taking a large statistics course who participate in an SI program.

b. The randomization eliminates any biases and ensures that the students in the SI group are as similar as possible to the students in the control group.

c. The comparison of the SI scores cannot be done if all the students are put in the treatment group.

Step by step solution

01

Given information

It is given that the students in a large statistics course are divided into the control group that will not participate in the supplemental instruction (SI)program and a treatment group that will participate in SI.

02

Check whether the scores from the SI group a sample from an existing population

a.

The scores from the SI group are not a sample from an existing population because the population is divided into control and treatment group.

The relevant conceptual population is,

All the students taking a large statistics course who participate in an SI program.

03

State the advantage of dividing the students into two groups.

b.

The advantage of randomly dividing the students into two groups rather than letting each student choose which group to join is that the randomization eliminates any biases and ensures that the students in the SI group are as similar as possible to the students in the control group.

04

Explain why all the students cannot be in the treatment group.

c.

All students cannot be put in the treatment group because there will be no criteria for assessing the effectiveness of the SI.

Therefore, the comparison of the SI scores can not be done if all the students are put in the treatment group.

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Most popular questions from this chapter

a. If a constant cis added to each \({x_i}\)in a sample, yielding \({y_i} = {x_i} + c\), how do the sample mean and median of the \({y_i}'s\)relate to the mean and median of the\({x_i}'s\)? Verify your conjectures.

b. If each \({x_i}\)is multiplied by a constant c,yielding \({y_i} = c{x_i}\), answer the question of part (a). Again, verify your conjectures.

As an example of a situation in which several different statis tics could reasonably be used to calculate a point estimate, consider a population of N invoices. Associated with each invoice is its 鈥渂ook value,鈥� the recorded amount of that invoice. Let T denote the total book value, a known amount. Some of these book values are erroneous. An audit will be carried out by randomly selecting n invoices and determining the audited (correct) value for each one. Suppose that the sample gives the following

\({\rm{T}}\)- sample mean book value

\(\bar X\)- sample mean advised value

\({\rm{\bar D}}\)- sample mean errors

Propose three different statistics for estimating the total audited (i.e., correct) value-one involving just N and,another involving T, N, and \({\rm{\bar D,}}\) and the last involving T and \({\rm{\bar X/\bar Y}}{\rm{.}}\)If \({\rm{N = 5000}}\)and T=1,761,300, calculate the three corresponding point estimates. (The article "Statistical Models and Analysis in Auditing," Statistical Science, 1989: 2-33 discusses properties of these estimators.)

An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records,\({\rm{20 \% }}\)of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. a. If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip? b. If six reservations are made, what is the expected number of available places when the limousine departs? c. Suppose the probability distribution of the number of reservations made is given in the accompanying table.

Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X.

A sample of n=10 automobiles was selected, and eachwas subjected to a 5-mph crash test. Denoting a car withno visible damage by S (for success) and a car with suchdamage by F, results were as follows:

S S F S SS F F S S

  1. What is the value of the sample proportion of successes x/n?
  2. Replace each S with a 1 and each F with a 0. Then calculate for this numerically coded sample. How does compare to x/n?
  3. Suppose it is decided to include 15 more cars in the experiment. How many of these would have to be S鈥檚 to give x/n = .80 for the entire sample of 25 cars?

For each of the following hypothetical populations, give

a plausible sample of size 4:

a. All distances that might result when you throw a football

b. Page lengths of books published 5 years from now

c. All possible earthquake-strength measurements (Richter scale) that might be recorded in California during the next year

d. All possible yields (in grams) from a certain chemical reaction carried out in a laboratory.
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