Question

HW9#8

Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and

d=x−​y,

find d overbard​, s Subscript dsd​,

the t test​ statistic, and the critical values to test the claim that μd=0.

x 10 14 6 4 7 11 16 6

y 11 11 9 9 9 12 11 7

over score d=    (round three decimal places)

Sd= (Round three decimal places)

t= (round three decimal places)

Ta/2=pluse sign with a bar under it (round to three decimal places)

Answer 1

Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
10	11	-1	0.140625
14	11	3	13.140625
6	9	-3	5.640625
4	9	-5	19.140625
7	9	-2	1.890625
11	12	-1	0.1406
16	11	5	31.6406
6	7	-1.0000	0.1406

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	74	79	-5	71.875

mean of difference ,    D̅ =ΣDi / n =   -0.625
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    3.204

Ho :   µd=   0
Ha :   µd ╪   0
std error , SE = Sd / √n =    3.2043   / √   8   =   1.1329      
                          
t-statistic = (D̅ - µd)/SE = (   -0.625   -   0   ) /    1.1329   =   -0.552

Degree of freedom, DF=   n - 1 =    7  
t-critical value , t* =    ±   2.365   [excel function: =t.inv.2t(α,df) ]
          

since, test stat=-0.552 >-2.365, do not reject Ho

There is not enough evidence to reject the claim