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Chapter 8: Q99SE (page 505)

Effectiveness of teaching software. The U.S. Department of Education (DOE) conducted a national study of the effectiveness of educational software. In one phase of the study, a sample of 1,516 first-grade students in classrooms that used educational software was compared with a sample of 1,103 first-grade students in classrooms that did not use the technology. In its Report to Congress, the DOE concluded that 鈥�(mean) test scores (of students on the SAT reading test) were not significantly higher in classrooms using reading 鈥� software products鈥� than in classrooms that did not use educational software.

a. Identify the parameter of interest to the DOE.

Short Answer

Expert verified

a. The parameter of interest is\({\mu _1} - {\mu _2}\).

Step by step solution

01

Given information

The sample size of first-grade students in classrooms that used education software is 1516.

The sample size of first-grade students in classrooms that didn鈥檛 use education software is 1103.

02

Defining the target parameters (parameter of interest).

If \({\mu _1}\) and \({\mu _2}\) are the two means of a population, and the type of the data is quantitative, then the target parameters of the mean difference can be represented\({\mu _1} - {\mu _2}\).

03

State the parameters of interest of the DOE.

Let \({\mu _1}\) be the mean test score of the first-grade students on the SAT reading test in classrooms that used educational software and \({\mu _2}\) be the mean test score of the first grade students on the SAT reading test in class rooms that didn鈥檛 use the educational software.

Therefore,

The parameter of interest is\({\mu _1} - {\mu _2}\).

i.e., The \({\mu _1} - {\mu _2}\) is the difference between the mean test score of the first grade students on the SAT reading test in classrooms that used educational software and didn鈥檛 use the educational software.

Hence, the parameter of interest is\({\mu _1} - {\mu _2}\).

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Most popular questions from this chapter

Hospital work-related injuries. According to an Occupational and Health Safety Administration (OHSA) 2014 report, a hospital is one of the most dangerous places to work. The major cause of injuries that resulted in missed work was overexertion. Almost half (48%) of the injuries that result in missed work were due to overexertion. Let x be the number of hospital-related injuries caused by overexertion.

a. Explain why x is approximately a binomial random variable.

b. Use the OHSA report to estimate p for the binomial random variable of part a.

c. Consider a random sample of 100 hospital workers who missed work due to an on-the-job injury. Use the p from part b to find the mean and standard deviation of, the proportion of the sampled workers who missed work due to overexertion.

d. Refer to part c. Find the probability that the sample proportion is less than .40.

Non-destructive evaluation. Non-destructive evaluation(NDE) describes methods that quantitatively characterize materials, tissues, and structures by non-invasive means, such as X-ray computed tomography, ultrasonic, and acoustic emission. Recently, NDE was used to detect defects in steel castings (JOM,May 2005). Assume that the probability that NDE detects a 鈥渉it鈥� (i.e., predicts a defect in a steel casting) when, in fact, a defect exists is .97. (This is often called the probability of detection.) Also assume that the probability that NDE detects a hit when, in fact, no defect exists is .005. (This is called the probability of a false call.) Past experience has shown a defect occurs once in every 100 steel castings. If NDE detects a hit for a particular steel casting, what is the probability that an actual defect exists?

The data for a random sample of six paired observations are shown in the next table.

a. Calculate the difference between each pair of observations by subtracting observation two from observation 1. Use the differences to calculate d炉andsd2.

b. If 渭1补苍诲渭2are the means of populations 1 and 2, respectively, expressed 渭din terms of 渭1补苍诲渭2.

PairSample from Population 1

(Observation 1)

Sample from Population 2(Observation 2)
123456739648417247

c. Form a 95% confidence interval for 渭d.

d. Test the null hypothesis H0:渭d=0against the alternative hypothesis Ha:渭d鈮�0. Use伪=.05 .

Given the following values of x, s, and n, form a 90% confidence interval for蟽2

a. x=21,s=2.5,n=50

b. x=1.3,s=0.02,n=15

c. x=167,s=31,n=22

d.x=9.4,s=1.5,n=5

Studies have established that rudeness in the workplace can lead to retaliatory and counterproductive behaviour. However, there has been little research on how rude behaviours influence a victim鈥檚 task performance. Such a study was conducted, and the results were published in the Academy of Management Journal (Oct. 2007). College students enrolled in a management course were randomly assigned to two experimental conditions: rudeness condition (students) and control group (students). Each student was asked to write down as many uses for a brick as possible in minutes. For those students in the rudeness condition, the facilitator displayed rudeness by generally berating students for being irresponsible and unprofessional (due to a late-arriving confederate). No comments were made about the late-arriving confederate to students in the control group. The number of different uses for brick was recorded for each student and is shown below. Conduct a statistical analysis (at 伪=0.01) to determine if the true mean performance level for students in the rudeness condition is lower than the actual mean performance level for students in the control group.

The data is given below

Control Group:

124516217201920191023160491317130212117311119912185213015421211101311361013161228191230


Rudeness Condition:

411181196511912757311191110789107114135478381591610071513921310
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