1.) Describe the general characteristics of a research study for which an independentMeasures t would be the appropriate test statistic.Independent t-test can be used to measure the difference between two groups wherein the groups are unrelated or independent of each other and where it is assumed that the variances in the two groups are equal, the dependent variable is normally distributed within each population and the data are independent from each other. An example of a research study that uses an independent t-test is when a school would like to test the difference in IQ scores of its male and female students.2.) What is measured by the estimated standard error that is used for theIndependent measures t statistic?The standard error for a difference in means is the standard error estimate used in independent-samples t-test. It is assumed that each sample mean contains errors; therefore the amount of error associated with each sample mean is measured by computing the standard errors for each sample and them adding the two standard errors. The standard error for a difference in means measures how much error is expected when we use a sample mean to represent a population mean.3.) Describe the homogeneity of variance assumption, and explain why it isImportant for the independent measures hypothesis test.One of the core assumptions of the independent t-test is that variances between the two samples must be equal, for the distribution must be normal and hence each score should not affect the other. If for example, variance is not equal, it would invalidate the t-test because the sample that has the greater number may increase the value of the mean for one of the sample.1.) For the following studies, indicate whether or not a repeated measures t test is the appropriate analysis. Explain your answers.a. A teacher is evaluating the effectiveness of a new computer training program for third-grade mathematics. One third-grade class gets regular mathematics instruction for 90 minutes each day. A second class gets the regular instruction 4 days each week, but on the fifth day spends 90 minutes working with the computer program. At the end of the school year, the teacher compares test scores for the two classes.No, the repeated measures t-test is not appropriate for this research because the teacher is trying to evaluate the effectiveness of the new computer program for third grade mathematics by comparing two groups, thus she is comparing two independent means where one was subjected to the computer program and the other group was not.b. A researcher is examining how light intensity influences colorPerception. A sample of 50 college students is obtained and eachStudent is asked to judge the differences between color patches under conditions of bright light and dim light.Yes, the repeated measures t-test is appropriate for this study since the researcher uses one group of participants and subjects them all to two conditions or treatments, that of bright and dim light.c. A research study compares problem solving ability for participants with two different levels of self esteem high self esteem and low self esteem.Yes, the repeated measures t-test is appropriate for this study since the researcher is now trying to test the difference in problem solving ability between two matched groups, high and low self-esteem.2.) What is the primary advantage of a repeated measures design over an independent measures design?The primary advantage of using a repeated measures design is that one can track or identify the change in the dependent variable as influenced by the independent variable because it uses the same group and wherein homogeneity of the variance is more clearly evident, it must be noted that using two-independent groups may mean that variances in score can be affected by the inherent characteristics of the sample.3.) Explain the difference between a matched-subjects design and a repeated measures design.A matched-subjects design refer to the kind of research wherein two groups are matched in one characteristic such as age, status, culture, educational background or even occupations, such as a study on the difference between Chinese and American students’ performance in a math achievement test. A repeated –measures design is when there is only one set of participants but is made to undergo different treatments or conditions, such as a pretest and posttest comparison of grade 4 students math scores.9.) A researcher uses a repeated measures study to evaluate the effectiveness ofMagnetic therapy for treating chronic pain. A sample of n = 9 patients is obtained,Each of whom has been treated for severe elbow pain for at least 1 year. EachPatient is given a questionnaire to evaluate the current level of pain. The patientsAre then instructed to wear a magnetic band around their elbows for 2 weeks.After the 2-week period, the patients again complete the questionnaire evaluatingPain. For this sample, the reported level of pain decreased by an average of MD =12.5 points with SS = 1152. Do these data indicate a significant change in theLevel of pain? Use a two-tailed test with a =.01. t = 3.125t critical at .01 alpha / df = 8 is 3.36Decision: There is no significant change in the level of pain that patients experienced.