Suppose that a recent article stated that the mean time spent in jail by a first

Question

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years with a standard deviation of 1.8 years. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal. State the null and alternative hypotheses.

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   2.5 years  
Ha:    u   >   2.5 years   [ANSWER]
              
As we can see, this is a    right   tailed test.  

*****************************

Other details:  
              
df = n - 1 =    25          
              
Getting the test statistic, as              
              
X = sample mean =    3          
uo = hypothesized mean =    2.5          
n = sample size =    26          
s = standard deviation =    1.5          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.699673171          
              
Hence, the p value is              
              
p =    0.05080173          
              
  

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.