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.
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.