Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those​ tests, with the measurements given in hic​ (standard head injury condition​ units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified​ requirement?

724    660     1157     575     552     442

Identify test statistic

identify P value

State conclusion

Answer 1

Null hypothesis     

           
                  
Alternative hypothesis  

              
                  
We have for given sample,                  
Population mean for given sample=1000  
Sample mean=685          
Sample standard deviation s=250.51      
Sample size =n=   6          
                  
Degree of freedom = n-1 =5  

   
t test statistic formula is

P value is 0.0137................................by using TDIST(-3.08, 5 , 1)

P value is 0.0137 < 0.05

Therefore , we reject H0.

Conclusion: We have sufficient evidence at to say that, the sample is from a population with a mean less than 1000 hic.