In a previous lab, data from a study conducted at a large university was presented. The study compared the effectiveness of two alternative teaching methods in first-year algebra courses: "Method 1" and "Method 2". To ensure that the selected methodology benefited all first-year students at the university, the committee conducted a randomized trial.

Three sections of the course were opened: one where a professor taught the material in a standard way, one where a professor taught using Method 1, and one where a professor taught using Method 2. These students were then randomly assigned to one of the three algebra courses but were not told that the methods of instruction varied. (Each method was assigned 100 students.) After the completion of these courses, the final grades of the students were compiled into a database. This database will then be used to decide which instructional method should be used in future classes.

Although the final grades associated with Method 1 appear higher than the grades of the Standard Method, can it be concluded at the 5% significance level that Method 1 is, in fact, better than the Standard Method?Two-sample hypothesis testing can be used to determine whether the difference in these sample means is significantly different. Use the techology of your choice to conduct a two-sample hypothesis test.

Data

The "comma separated variable" (csv) file containing (fictitious) students' final grades is included on Blackboard. It is entitled "TestScores.csv" and can be downloaded. This dataset contains 300 values divided into three columns: standard method, new method 1, and new method 2. These labels correspond to the teaching strategies implemented in the scenario described above. Use descriptive statistics to characterize these data and draw conclusions. (Get data here:TestScores(2).csv)

Scenario

In a previous assignment, a professor's claim that the average score in this first-year course is typically 78% was tested. Here, statistical rigor will be used to say, definitively, that "Method 1" is actually better (or not). The tool to be used is the two-sample hypothesis test.

Final Note

You may use any method or technology to perform necessary calculations. Excel can be used to calculate the sample mean and standard deviation of the data (be sure to use the correct column: "Standard Method"). R has a command to perform a two-sample t-test that will handle all of the calculations. If you would like to use R, see the comments below.

R command: t.test(x, y, mu, alternative)

Here, the first and second arguments,xandy, must be vectors of your data. (In this case, it will be a the final grades from the "Standard Method" of teaching and the final grades for "Method 1" of teaching. Information on how to create these vectors can be found in previous labs.)

muis the theoretical (or assumed) mean. In this case, we first assume that there is no difference between the means, somu=0.

alternativehas three possible inputs: alternative = "two.sided", alternative = "greater", alternative = "less". Selecting one of these indicates whether you want to test for ANY significant difference, if the sample mean of xis greater than the assumed mean, or if the sample mean of xis less than the assumed mean.

(Additional information:Unpaired Two-Samples T-test in R - Easy Guides - Wiki - STHDA)

Useful Tool: t-Distribution Calculator

1. Identify the correct null and alternative hypotheses.