Question

A new car dealer calculates that the dealership must average more than 4.5% profit on sales of new cars. A random sample of 81 cars yielded a sample mean of 4.97% profit and a sample standard deviation of 1.8%. Using a significance level of α = .05, does the sample data provide evidence to conclude that the dealership averages more than 4.5% profit on sales of new cars?

A. Yes, because the the sample mean is more than 4.5%.

B. Yes, because p = .0106 is less than .05.

C. No, because t = 2.35 is more than 1.645

D. No, because the p-value is less than the critical value

Answer 1

B. Yes, because p = .0106 is less than .05.

Null hypothesis         

   
              
Alternative hypothesis  

           
              
We have for given sample,              
Population mean for given sample=4.5
Sample mean=4.97      
Sample standard deviation s=1.8  
Sample size =n=   81      
              
Degree of freedom = n-1 =80

t test statistic formula is              

P value is = 0.0106......................by using Excel command TDIST(2.35, 80 , 1)

P value is = 0.0106 < 0.05