MATH219: Statistics and Probability - Export Images - Statistics Assignment Help

Assignment Task:

Task:

You should submit a single document, preferably a .pdf, with your name, student number, and “MATH219 Assignment 3” at the top. Put the question number at the start of the section that answers that question. Export images from your favourite stats package and embed them in the page to talk about them. You should take the results that you get from computations and put them in the document as well, but tell me what they are. So if you compute a sample mean of 5.43, tell me “the sample mean was 5.43” or something similar. In all cases, complete your calculations with a large number of decimal places but only report the answers to 2 decimal places. Your answers should be complete sentences as much as possible.

10. You have been asked to assess the effectiveness of a new teaching tool. A sample of 25 students from your classes have been tested before and after the provision of the tool, so each student has two measurements associated with them.

You are testing:
(a) Has the teaching tool changed student performance?
(b) Is there more variability in the tool’s effect than you want?

To collect your dataset, download the Assignment3.xlsx dataset from LEO and take the 25 rows labelled with your student number. For the purpose of this assessment you can assume that your data is as normally distributed as you need it to be. The third column in this dataset corresponds to the σ 2 0

value necessary for part (b).
For each of these tests provide the following:

(i) What are H0 and HA?
(ii) What is the test statistic, and under the null hypothesis what is its sampling distribution?
(iii) Determine the region of rejection for α = 0.05.
(iv) Is your test statistic in the region of rejection? Write a sentence or two about the determination.
(v) Using Excel, R, or otherwise calculate the p-value.
(vi) What can you conclude about your hypotheses from the p-value with respect to α = 0.05?
(vii) Build a 95% CI that corresponds to the hypotheses.

Finally
(c) Produce a histogram of the sample differences that you used for part (a).

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