Reference no: EM132267548

Lab Assignment - Inferences For Numerical Data

In this lab assignment, you will first use the analysis of variance tool available in StatCrunch to explore how different teaching strategies affect learning. You will use the one-way ANOVA F-test to test the hypothesis that the midterm score is not affected by different teaching strategies, comprised of different combinations of homework assignments, weekly quizzes, and computer tutorials. Moreover, you will examine the effect of a variety of teaching strategies on the exam scores. Before you start working on the assignment, you should review the course material about one-way ANOVA as well as two-sample inferences and familiarize yourself with Lab Instructions (attached).

A Comparison of Teaching Strategies -

In any learning environment, there are several different teaching strategies. These strategies (which can be composed of several components such as homework, quizzes, computer aid, and others) may depend on several factors, such as the teacher's preference, availability of resources, or time constraints. Thus, it is of interest to determine which strategies or components are most effective. The goal of this study is to compare several strategies for high school math that incorporate three common components (homework assignments (H), weekly quizzes (Q), and computer tutorials (T)), examining which strategies are most effective. The experiment was conducted on Math 30 students from a large high school. All 120 students available were randomly assigned to one of six different teaching strategies. The randomization ensured an equal number to each group. The six different groups to consider are as follows:

Group 1: C (control group, only lecture notes and discussion)

Group 2: H (control plus weekly homework assignments)

Group 3: Q (control plus weekly quizzes)

Group 4: T (control plus computer tutorials)

Group 5: HT (control plus weekly homework as well as computer tutorials)

Group 6: QT (control plus weekly quizzes well as computer tutorials)

Note: It was determined that both weekly quizzes and homework assignments were too much to handle. Thus, there are two group combinations missing, HQ and HQT.

The study was conducted over the first half of the term with the response variable being the student score on the midterm (out of 100) on a standardized test. To ensure equality, the midterm was conducted for all students at the same time in a large gymnasium. The primary goal of this study is to determine if there is a difference in student achievement based on the different teaching methods. If so, which components (homework, quizzes, and computer tutorials) have the greatest impact on learning? All students were taught using the exact same set of course notes.

The data are attached. The data are not to be printed in your submission.

The following is a description of the first two variables in the data file:

Column	Variable Name	Description of Variable
1	Strategy	teaching strategy: C, H, Q, T, HT, QT
2	Code	teaching strategy: 1 = C, 2 = H, 3 = Q, 4 = T, 5 = HT, 6 = QT
3	Score	midterm score (out of 100)

Use the data to answer the following questions:

Study Design -

1. First describe the study and examine the study design.

(a) What is the population of interest? Who are the subjects used in the study? What is the response variable? What is the factor in the study? What are the levels of the factor?

(b) Comment on the study design. What kind of inferences can be drawn about the factor? Can the study be used to prove that the different teaching strategies cause the observed differences in midterm scores? Can any inferences be drawn about the population?

Exploratory Data Analysis -

2. Before applying any inferential tools to the data, always conduct a preliminary analysis to get an idea about the association between your variables. In addition, the results of a statistical analysis are valid only if the appropriate assumptions for the model to be used are valid. The assumptions for the ANOVA are that the data are independent and come from normal populations with equal variances (or standard deviations). In particular:

(a) Obtain the summary statistics (sample size, mean, standard deviation, and variance) for each group. Paste the results into your report. Compare the means of the six groups. Which strategy seems the best? The worst? Compare the standard deviations of the six groups. Does it appear that the assumption of equal variability is satisfied?

(b) Obtain and paste the side-by-side boxplots into your report. Check the "Use fences to identify outliers" and "Draw boxes horizontally" options. Comment on the shape (symmetric, skewed) of each distribution. Do the plots indicate any differences in the centers and spreads among the six groups? Are there any unusual observations (outliers)? Do the boxplots indicate any clear violation of the assumption of normal populations?

(c) Does it appear that the ANOVA F-test is valid given the results in parts (a) and (b)? Explain briefly.

Inference -

3. Is there sufficient evidence that average midterm scores differ between the different teaching strategies? Answer the question by running the one-way ANOVA test in StatCrunch.

(a) Paste the ANOVA output into your report.

(b) Define the null and alternative hypotheses in terms of the population means. What is the pooled estimate of the common population variance? What is the value of the test statistic and P-value? What is the null distribution of the test statistic? Based on the P-value, is there sufficient evidence to indicate any difference among the six teaching strategies?

4. Is there sufficient evidence that weekly homework assignments (in addition to lecture notes and discussion) increased the midterm scores, on average? (Consider only groups required to answer the question; there is no need to factor in the other groups; in other words, ignore the groups not included.)

(a) Carry out the appropriate test to answer the question. Paste the corresponding StatCrunch output into your report.

NOTE: Pool the variances in (a) and (b) if justified by the summary statistics provided in Question 2. Explain briefly your choice of inferences with or without pooled variances.

Define the null and alternative hypotheses in terms of the population means. What is the value of the test statistic and P-value? What is the null distribution of the test statistic? Based on the P- value, is there sufficient evidence to indicate a beneficial effect of weekly homework assignments on the midterm scores?

(b) Estimate the effect of weekly homework assignments on the midterm scores with a 95% confidence interval. Is the interval consistent with the outcome of the test in part (a)?

5. Is there sufficient evidence that weekly quizzes have any effect on the midterm scores for groups with computer tutorials, on average? (Consider only groups required to answer the question; there is no need to factor in the other groups; in other words, ignore the groups not included.)

(a) Carry out the appropriate test to answer the question. Paste the corresponding StatCrunch output into your report.

NOTE: Pool the variances in (a) and (b) if justified by the summary statistics provided in Question 2. Explain briefly your choice of inferences with or without pooled variances.

Define the null and alternative hypotheses in terms of the population means. What is the value of the test statistic and P-value? What is the null distribution of the test statistic? Based on the P- value, is there sufficient evidence to indicate any effect of weekly quizzes on the midterm scores for groups with computer tutorials?

(b) Given the outcome of the test in part (a), what do you expect of a 95% confidence interval for the mean difference in midterm scores for the two groups? You may obtain the confidence interval to verify your conclusion but do not report it in your submission.

Attachment:- Assignment Files.rar