Question

6. Assume that you wanted to know whether the average FAU graduate spends more days looking for a job after graduation than the nationwide average for college graduates of 150 days. If you sampled FAU students and found that 10 of them produced the following data (120, 130, 250, 125, 175, 200, 100, 260, 340, 300), what would you conclude? Conduct a one-sample t-test and report your t-statistic, critical value, and decision on whether to reject your null hypothesis to answer this question.

Answer 1

Null hypothesis

$H_{0}:\mu =150$

Alternative hypothesis

$H_{1}:\mu >150$

We have for given sample,

Population mean for given sample=150

Sample mean=200

Sample standard deviation s= 83.8318

Sample size =n= 10

Degree of freedom = n-1 =9

t critical value for right tailed test with degree of freedom n-1 = 9 and level of significance 0.05 is 1.833

Decision rule: Reject H0 if t calculated > t critical value

t test statistic formula is

$=t=\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}=\frac{200-150 }{\frac{83.8318}{\sqrt{10}}}$

= 1.886

t calculated value > t critical value

Therefore, we reject H0.

We have sufficient evidence to say that, the average FAU graduate spends more days looking for a job after graduation than the nationwide average for college graduates of 150 days.