Homework 3: Professor Ozer

October 29th

Question 1

Which of these countries has the most stable voter turnout rate? Why?

United States of Coconut has the most stable voter turnout rate. For this country the variation between elections is smaller, that is 2 standard deviations about the mean hence more stable compared to the other countries with 10 standard deviations about the mean.

b. Calculate the 95% confidence interval for each country. Please report them in the

following format: [lower bound, upper bound]

A 95% confidence limit refers to 2 standard deviations about the mean.

Country Upper bound Lower bound

Ozeristan 58.76 41.24

Democratic Republic of Fisher 68.76 51.24

United States of Coconut71.75 68.25

Does the evidence support Hypothesis 1? Why or why not?

The evidence rejects hypothesis 1 since from the evidence the Democratic Republic of Fisher has a higher mean voter turnout on average that the Ozeristan considering they have a similar standard deviation and sample size used is the same size.

Does the evidence support Hypothesis 2? Why or why not?

The evidence supports hypothesis 2 since the United States of Coconut has a higher mean voter turnout on average than the other two countries.

What would happen if we increased the sample size to 10 elections? 100 elections?

Considering the sample is a representation of the general population, the mean voter turnout and standard deviation will remain the same, same values as before. The initial sample is a representation of the general population thus the results remain unchanged.

Question 2

a. What does it mean for something to be “statistically significant”?

It means that the activity did not occur by accident and hence the probability of that event occurring is usually low (p<0.5) and hence when it occurs it is not by chance.

b. What does it mean for something to be “substantively significant”?

It means the event or activity has a size large enough to have meaning that is the event does not only have a low probability of occurring but also has a size that could have an impact on a study/research.

c. If something is statistically significant, does that mean its also substantively

significant? Why or why not?

No. any event can be statistically significant as long as it had a low probability of occurring (p<0.5) but for it to be substantively significant it must also possess a size large enough to have meaning. Thus, all substantively significant events are statistically significant but not all statistically significant events are substantively significant.

d. Why are null findings still important and relevant?

Null findings and hypothesis, in general, are still important and relevant as they provide the researcher with a description to test and hence the experiment has a guiding tool. They are very important especially in novel experiments where the researcher does not know what to expect.

Question 3

Calculate a difference of means test.

Using the formulas;

Results

Difference -25

Standard error 2.121

95% confidence limit -29.1833 to -20.8167

t-statistic -11.785

DF 198

Significance level P<0.0001

b. Is there a statistically significant difference between the two groups (p<.05)? Why?

There is a statistically significant difference between the two means since the p-value is below 0.05. hence the null hypothesis is rejected.

Bonus question! (.5 points)

Who/what are you going as for Halloween?

I am thinking about going as myself but have not yet decided, still have a Lilo and stitch costume theme (Disney characters) at the back of my head