Question

The United States government claims DUI arrests average 32,096 per state per year. A sample of size n=20 states finds the mean to be 44,002. If DUI arrests are normally distributed with a standard deviation of 28,584. Develop null and alternative hypothesis that will help deciding whether DUI arrests are higher than government claims at the 1% significance level and calculate the p value? Question 18 options:

0.0390

0.0008

0.2345

0.3546

Answer 1

Null hypothesis      

       
              
Alternative hypothesis  

           
              
We have for given sample,              
Population mean for given sample=32096
Sample mean=44002      
Sample standard deviation s=28584  
Sample size =n=   20      
              
Degree of freedom = n-1 =19  
              
              
              
t test statistic formula is              

P value is = 0.0390......................by using Excel command TDIST(1.8628,19,1)