Question

Do brain growth patterns indicate autism in toddlerhood, before a diagnosis of autism can be made? One study looked at the brain sizes of 30 autistic boys who had received an MRI scan as toddlers. Their whole-brain volumes in ml were recorded, and summary statistics are displayed below. It is known that toddlers without autism have an average brain volume of 1179 ml, and researchers wanted to know whether autistic toddlers’ brain volumes were different, on average.

n=30 mean=1298 standard deviation=88.412 standard error=16.142

Calculate the test statistic for this hypothesis test and specify the probability model for the test statistic.

a) z = 7.372, standard normal distribution

b) t = 7.372, t-distribution with df=29

c) t = 2.113, t-distribution with df=29

d) z = 40.379, standard normal distribution

e) t = 40.379, t-distribution with df=29

Answer 1

We have for given sample,                  
Population mean for given sample=1179  
Sample mean=1298          
Sample standard deviation s=88.412      
Sample size =n=30          
                  
Degree of freedom = n-1 =29      
                  

                  
t test statistic formula is
  

b) t = 7.372, t-distribution with df=29