Which, for purely pedagogical reasons, we have no credible state (a known population variance) is behind us, we turn our attention to the realistic situation of the population means and population differences is unknown.
Now we Explain it with Example:
Example:
| Ten individuals are choosen at rendom from a normal population and the hights are found to be inches | ||||||||||
| 63,63,66,67,68,69,70,70,71,and71in the light of these data disscuss the suggestion that mean hight | ||||||||||
| in population is 66 inches | ||||||||||
63
63
66
67
68
69
70
70
71
71
| mean | 67.8 | |
| s | 3.011091 | |
| n | 10 | |
| d.f | n-1 | 9 |
For two sided test
Formulas:
T = X̅- μo/(s/ √n )
t-cal = X̅- μo/(s/sqrt(n) )
t-tab =(TINV((Probability,d.f))
p-value=TDIST(ABS(t-cal),d.f,2)
 |
| population is normal Variance is un known for two sided |
For One sided test:
Upper Tail
Formulas:
T = X̅- μo/(s/ √n )
t-cal = X̅- μo/(s/sqrt(n) )
t-tab =(TINV((Probability,d.f))
p-value=TDIST(ABS(t-cal),d.f,1)
1- p value = 1- TDIST(ABS(t-cal),d.f,1)
Decission of C.R =if(t-cal<0,1-p value, p-value)
 |
| population is normal Variance is un known for one sided upper tail |
Lower Tail
Formulas:
T = X̅- μo/(s/ √n )
t-cal = X̅- μo/(s/sqrt(n) )
t-tab =(TINV((Probability,d.f))
p-value=TDIST(ABS(t-cal),d.f,1)
1- p value = 1- TDIST(ABS(t-cal),d.f,1)
Decission of C.R =if(t-cal<0,1-p value, p-value)
 |
| population is normal Variance is un known for one sided Lower tail |
