a bank with a branch located in a commercial district of a city has the business

Question

a bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1 pm lunch period, Management decides to first study the waiting time in the current process. The waiting time is defined as the the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window.

a. assuming that the population variances from both banks are equal is there evideince of a difference in the mean waiting time between the teo branches(use a -0.05)

b. determine the p-value in (a) and interpret its meaning.

c. In addition to equal variances, what other assumption is necessary in (a)?

please show the work

thank you

Bank 1 Bank 2 4.21 9.66 5.55 1.9 3.02 8.02 5.13 2.79 4.77 8.73 2.34 3.82 3.54 8.01 3.2 8.35 4.5 10.49 6.1 6.68 0.38 5.64 6.12 4.08 6.46 6.17 6.19 9.91 4.79 5.47

Explanation / Answer

Given that,
mean(x)=4.42
standard deviation , s.d1=1.6896
number(n1)=15
y(mean)=6.648
standard deviation, s.d2 =2.6739
number(n2)=15
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.048
since our test is two-tailed
reject Ho, if to < -2.048 OR if to > 2.048
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (14*2.855 + 14*7.15) / (30- 2 )
s^2 = 5.002
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=4.42-6.648/sqrt((5.002( 1 /15+ 1/15 ))
to=-2.228/0.817
to=-2.728
| to | =2.728
critical value
the value of |t | with (n1+n2-2) i.e 28 d.f is 2.048
we got |to| = 2.728 & | t | = 2.048
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - ha : ( p != -2.7282 ) = 0.0107
hence value of p0.05 > 0.0107,here we reject Ho
ANSWERS
---------------
a.
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -2.728
critical value: -2.048 , 2.048
decision: reject Ho
b.
p-value: 0.0107
we have enough evidence to support the claim that difference in the mean waiting time between the teo branches
c.
no assumptions for part (a) because already we done population variances are equal

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