Please Help me Solve This Statistics Problem

Question

Conduct a two-sample t-test to determine if college freshman and seniors have a significantly different number of speeding tickets. Using the data below, counduct a two-sample t-test. Show your work.

Freshman: 2, 1, 4, 2, 5, 1, 0, 2, 4, 2

Seniors: 1, 2, 1, 1, 0, 2, 1, 0, 1, 2

What are the results of the test?

Are the results statistically significant?

What does this imply for freshman and seniors?

Answer 1

Hi Sarah,

I know a couple ways to do this. The first and simplest would be if you had a TI-83 or greater calculator. In that case, you would go to:

STAT-Edit-L1--enter all values for freshmen

STAT-Edit-L2-enter all values for seniors

Then, go to STAT-TESTS-2-SampTTest. Do not change any settings. The calculator will then return your t-test statistic, degrees of freedom, and p-value. Generally, the p-value cutoff (alpha) for statistical significance is 0.05. Check your p-value against this. If smaller, result is significant and freshmen and seniors have significantly different numbers of speeding tickets on average. If not, you do not have evidence of significant difference.

The longer way:

t=(xbar₁-xbar₂)-D/sqrt[(s₁²/n₁) + (s₂²/n₂)]

xbar1=first sample mean--add all values of freshmen; divide by 10

xbar2=second sample mean--add all values of seniors and divide by 10

D=hypothesized difference = 0

S₁=first sample standard deviation--best to compute by calculator or software

S₂=second sample standard deviation--best to compute by calculator or software

n₁=first sample size = 10

n₂=second sample size = 10

Conservative estimate of degrees of freedom (df) is n - 1 = 9

Once you have t, check the t-table and see where that t-test statistic falls. This will give you an estimate for p-value, which you can use the same criteria as above to decide significance.

I hope this helps.