Find and report the sample means and variances

Reference no: EM131902955

Tennessee's Project STAR

A longitudinal experiment was conducted in Tennessee beginning in 1985 and ending in 1989. A single cohort of students was followed from kindergarten through third grade. In the experiment children were randomly assigned within schools into three types of classes:

1. small classes with 13-17 students,

2. regular-sized classes with 22-25 students, and

3. regular-sized classes with a full-time teacher aide to assist the teacher.

Student scores on achievement tests for maths and reading were recorded, as was some information about the students, teachers, and school. A subsample of the data on achievement tests' scores is contained in the EViews file star.wf1.

The series in this file are:

math_aide maths score in regular class with a teacher aide math_reg maths score in regular class without a teacher aide math_small maths score in a small class

read_aide reading score in regular class with a teacher aide read_reg reading score in regular class without a teacher aide read_small reading score in a small class

Begin by creating three new series, say total_aide, total_reg, and total_small, which are equal to the sums of the maths and reading scores.

Among other things, we wish to investigate whether (a) having a teacher aide improves total scores, and (b) whether having a small class improves total scores.

Question 1

(a) Find and report the sample means and variances for total_aide and total_reg.

(b) Find the ratio of the two sample variances in (a).

(c) The ratio in (b) can be used to test a null hypothesis. What is that null hypothesis? Be sure to define your notation.

(d) Find the p-value of the test outcome from (b) and (c). Assume a two-tail test.

(e) Assuming a 10% significance level, what is the outcome of the test?

(f) Use EViews to find the exact critical values of the test.

(g) Find a pooled variance estimate under the assumption that the null hypothesis in (b) is true.

Question 2

This question is concerned with testing whether the mean total score for classes with a teacher aide is greater than the mean total score for regular-sized classes without a teacher aide.

(a) Specify suitable null and alternative hypotheses. Be sure to define your notation.

(b) Using information from Question 1 parts (a) and (g), compute the value of the relevant test statistic.

(d) At a 5% significance level, what is your test conclusion?

(e) Use EViews to find the exact test critical value.

Question 3

This question is concerned with testing whether the mean total score for small-sized classes is greater than the mean total score for regular-sized classes (without a teacher aide).

Use EViews to carry out this test. Include your EViews output. Report your findings.

(There is no need to give step-by-step details. Simply report your findings in two sentences. The first in language you might use for a statistician, and the second in language you might use for the parents of the children in the schools.)

Question 4

Consider the maths scores and reading scores for students in small classes.

(a) Find and report the sample means, variances, and covariance for these two scores.

(b) Find the difference in the sample means and an estimate of the variance of this difference.

(c) Find a 95% interval estimate (confidence interval) for the population difference in the means for maths and reading scores in small classes.

(d) Report the Jarque-Bera p-values for each of the two series. Is it reasonable to assume they come from normal distributions? Comment on the relative shapes of the two histograms. (Include the EViews histograms in your answer.)

Attachment:- star-2.rar

Reference no: EM131902955

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len1902955

3/15/2018 3:59:54 AM

A separate link will be given to submit your assignment on 22, after the assignment group registration process is completed. • For assignments submitted as a group, both group members will receive the same mark for the assignment. Students should form their own groups. No credit can be given for group assignments where members of the group do not come from the same tutorial, or where there are more than two students in a group. • All assignments should be converted into PDF before submitting online via the LMS. Students must preview their assignment after uploading on the LMS to ensure they have uploaded the correct/complete assignment, and the formatting is in order as in their original document. Submissions that are late because of formatting issues, or because a version is incomplete, will not be accepted. • Please make sure to include a cover page with student IDs and names of both group members.

len1902955

3/15/2018 3:59:43 AM

• Please note that the assignment submission process has two stages: 1. Registering your assignment group, and 2. Submitting the assignment online via the LMS. To register your group, go to the link that will be placed on the LMS and follow the instructions. The deadline for registering your group is 5:00 PM on Wednesday 21. Students making an individual submission do not have to register: single-member groups are created automatically after group registration has closed. If a pair fails to register their group before the deadline for group registration, both students will need to make an individual submission.

len1902955

3/15/2018 3:59:38 AM

Please read the following instructions carefully before working on the assignment. There is a total of 85 marks for this assignment. It is worth 5% of the final grade for QM2. • This assignment must be submitted online via the LMS by 4:00 PM on Monday 26. Any assignment not submitted by this due date and time will be given a mark of zero. • A group of two students (but no more than two students) may work together and submit one set of assignment answers for the group. Both members of the group must be enrolled in the same tutorial. Individuals may work alone if they wish, and submit their own assignment answers, but I urge students to work in pairs.

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