Question

1. Ten epileptic patients participated in a study of a new anticonvulsant drug, valproate.  During an 8-week placebo period, the number of epileptic seizures were counted for each patient. After this, each patient was then given Valproate, and seizure counts were made during a second 8-week period.  The number of seizures are given below:

Patient	Placebo	Valproate
1	37	5
2	52	22
3	63	41
4	2	4
5	25	32
6	29	20
7	15	10
8	52	25
9	19	17
10	12	14

The number of seizures during the placebo period come from a normal distribution with mean µ₁ and variance .

The number of seizures during the Valproate period come from a normal distribution with mean µ₂ and variance .

Perform a hypothesis test at the 5% significance level to determine if the mean number of seizures is lower with Valproate than with the placebo.  Give hypotheses, test statistic, P-value, conclusion, and interpretation.

Answer 1

paired t test

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
37	5	32	416.160
52	22	30	338.560
63	41	22	108.160
2	4	-2	184.960
25	32	-7	345.960
29	20	9	6.760
15	10	5	43.560
52	25	27	237.160
19	17	2	92.160
12	14	-2	184.960

Ho :   µd=   0
Ha :   µd >   0

mean of difference ,    D̅ =ΣDi / n =   11.600                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    14.751                  
                          
std error , SE = Sd / √n =    14.7513   / √   10   =   4.6648      
                          
t-statistic = (D̅ - µd)/SE = (   11.6   -   0   ) /    4.6648   =   2.4867
                          
Degree of freedom, DF=   n - 1 =    9                  
t-critical value , t* =        1.8331   [excel function: =t.inv(α,df) ]               
                          
p-value =        0.0173   [excel function: =t.dist.rt(t-stat,df) ]               
Decision:   p-value <α , Reject null hypothesis                      

there is enough evidence to conlcude that the mean number of seizures is lower with Valproate than with the placebo.