STAT1020- Statistical Reasoning and Literacy

Task:

PART A: Short Answer Questions

1) A difficult exam in which most of the class did poor would form what shaped distribution? Justify your answer.

2) If two populations are different on their population means and the inferential statistical test leads you to conclude that the populations are not different, you have committed what type of error?

Justify your answer 

3) What is the p value of a test?

4) If the results state that differences are statistically significant, what does this mean? 

PART B: Scenario Based Questions 

5) Does eating oatmeal reduce the level of bad cholesterol (LDP)? Here are two ways to study this question.

Scenario A. A researcher finds 500 adults over 40 who regularly eat oatmeal or products made from oatmeal. She matches each with a similar adult who does not regularly eat oatmeal or products made from oatmeal. She measures the bad cholesterol (LDL) for each adult and compares both groups.

Scenario B. Another researcher finds 1000 adults over 40 who do not regularly eat oatmeal or products made from oatmeal and are willing to participate in a study. She assigns 500 of these to a diet that includes a daily breakfast of oatmeal. The other 500 continue their usual habits. After 6 months she compares changes in LDL levels.

a) Identify the study type of scenario A (observational or experimental). Explain your reasoning.

b) Identify the study type of scenario B (observational or experimental). Explain your reasoning.

c) Which design do you think would be more effective at demonstrating the effects of Oatmeal on LDL levels? Why? 

d) Identify the explanatory (X) variable and the response (Y) variable. Justify your answer.

e) The data for scenario B revealed that for those on the oatmeal diet, the reduction in LDL 

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was on average 12 units, while for those who did not regularly eat oatmeal, the reduction in LDL was on average 8units.

i) What would be the appropriate statistical test to use to determine if oatmeal was more effective in reducing LDL levels compared with a diet without oatmeal? Explainwhy. 

ii) State the null and alternative hypothesis for the proposed test. 

iii) What do the summary statistics presented in part e) suggest about the effectiveness of the oatmeal diet? Are these figures enough to make a  conclusive statement? Explain why or why not.

iv) Assume the hypothesis test resulted in a p-value of 0.03. Make a conclusion based on this p-value, including your decision with regards to the null hypothesis.

6) A speech therapist tests whether different workshops increase articulation rates of children. A total of 32 subjects are randomly assigned to attend either B, C or D type workshop sessions or to a control group A.

The results (expressed as the observed number of words articulated in a given time interval) were recorded and are shown in the table below.

Number of Words Articulated

Workshop:

A 0 1 0 3 1 2 4 2

B 1 3 2 2 4 6 3 4

C 5 4 7 8 6 3 2 5

D 7 1 6 9 10 12 8 7

An analysis of the data using JMP yielded the output shown on the next page.

a) What do the Boxplots and Means for each group suggest about the effectiveness of the workshops. These are reported in the output above.

b) Which statistical test should be used to address the objective and why.

c) State the null and alternative hypothesis for this test. 

d) Report the appropriate value of the test statistic from the output above.

e) From the output above, the p-value is reported as <0.0001. Use this p-value to make a decision regarding the null hypothesis and make a conclusion. 

f) Is the result in part e) suffice to determine which workshops are more effective? If not, which test should be used to determine where the differences are.