Question

Sometimes the extent to which two groups differ is quite obvious. For example, if one group of individuals has an average of 20 speeding tickets, while another group has an average of 2, we can be pretty sure that the difference is statistically significant. But sometimes it is less clear. What if one group had an average of 10, while the other had an average of 7? T-tests provide a way to determine if differences between means are enough to be statistically significant.

Freshmen and Seniors

For this assignment, you will conduct a two-sample t-test to determine if freshmen and seniors have a significantly different number of speeding tickets. Using the data provided below, conduct a two-sample t-test.

Speeding Tickets for Freshmen and Seniors

Freshmen	Seniors
4	1
3	2
5	1
4	1
6	0
3	2
2	1
4	0
5	1
4	2

Then, create a summary of 1-2 paragraphs in which you address the following:

• Present the result of the two-sample t-test.
• Explain whether or not the result is statistically significant.
• Discuss what this implies for freshmen and seniors, and whether or not the results fit with your own expectations.

Be sure to include supporting detail from the readings, as well as other scholarly sources.

Answer 1

The results of the two-sample t-test are:

The equal variance assumption is met for this analysis. So the pooled variance sample t-test is being conducted here.

The results are statistically significant.

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that freshmen and seniors have a significantly different number of speeding tickets.

We have evidence for our sample that Freshmen students get more speeding tickets than Seniors. Also, the variation in the speeding tickets is more for Freshmens than Seniors.