Answer:
The confidence Interval is [- 0.7053  10.4521]
a: The  hypotheses  are 
H0: μ1=μ2    against the claim Ha :μ1≠μ2
b. The critical value for t∝/2 for 17 d.f  t > 2.508 and  t < -2.111
c. t= -2.8422
d. The calculated value of t= -2.8422 is less than t < -2.11 the critical value therefore we reject H0 and conclude there is a difference between the two means. 
Step-by-step explanation:
When the standard deviations are not the same then the confidence intervals for mean differences are calculated as 
(x1`-x2`)- t∝/2 √s1²/n1 + s2²/n2 < u1-u2 < (x1`-x2`)+ t∝/2 √s1²/n1 + s2²/n2
x1`= 21        x2`= 27
n1=  10       n2= 14
s1= 5.6       s2= 4.3
The degrees of freedom is calculated using 
υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1
= 17
The t∝/2 for 17 d.f = 2.11
Putting the values 
(x1`-x2`)- t∝/2 √s1²/n1 + s2²/n2 < u1-u2 < (x1`-x2`)+ t∝/2 √s1²/n1 + s2²/n2
(21-27) - 2.11√5.6²/10+ 4.3²/14 < u1-u2 <(21-27)  +2.11√5.6²/10+4.3²/14 
6- 2.11*2.111 < u1-u2 <  ( 6 )  +2.11*2.111
6- 4.4521 < u1-u2 <  ( 6 )  +5.294
- 1.5479 < u1-u2 <  10.4521
The confidence Interval is [- 0.7053  10.4521]
a: The  hypotheses  are 
H0: μ1=μ2    against the claim Ha :μ1≠μ2
The claim is that there is a difference in the average time spent by the two services 
b. The critical value for t∝/2 for 17 d.f  t > 2.508 and  t < -2.111
The degrees of freedom is calculated using 
υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1
= 17
c. The test statistic is 
t= (x1`-x2`)  /√s1²/n1 + s2²/n2
t= (21-27)  /√5.6²/10+ 4.3²/14
t= -6/2.111
t= -2.8422
d. The calculated value of t= -2.8422 is less than t < -2.11 the critical value therefore we reject H0 and conclude there is a difference between the two means.