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? Z-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 z-test to determine if freshmen and seniors have a significantly different number of speeding tickets. Using the data provided below, conduct a two-sample z-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 Are the results statistically significant? What does this imply for freshman and seniors?

Answer 1

: Mean number of speeding tickets for Freshmen

: Mean number of speeding tickets for Seniors

Null hypothesis : - = 0

Alternate Hypothesis : H_a : (Two tailed hypothesis)

Sample 1 : Speeding tickets for Freshmen

Sample 2 : Speeding tickets for Seniors

n₁ : sample size of Freshmen = 10

Sample mean of speeding tickets for Freshmen:

Sample standard deviation of speeding tickets for Freshmen:

n₁ : sample size of seniors= 10

Sample mean of speeding tickets for seniors:

Sample standard deviation of speeding tickets for seniors:

	x1: Freshmen	)			x2: Seniors
	4	0	0		1	-0.1	0.01
	3	-1	1		2	0.9	0.81
	5	1	1		1	-0.1	0.01
	4	0	0		1	-0.1	0.01
	6	2	4		0	-1.1	1.21
	3	-1	1		2	0.9	0.81
	2	-2	4		1	-0.1	0.01
	4	0	0		0	-1.1	1.21
	5	1	1		1	-0.1	0.01
	4	0	0		2	0.9	0.81
Total	40		12		11		4.9
Mean : =40/10 =4				Mean : =11/10 =1.1

For two tailed test :

Level of significance : 0.05

As P-Value i.e. is less than Level of significance i.e (P-value:0 < 0.05:Level of significance); Reject Null Hypothesis
There is sufficient evidence to conclude that the differences between means is statistically significant.

Difference in  the mean number of speeding tickets for Freshmen and mean number of speeding tickets for seniors is significant.