option for (b): more lor less than 0.05, reject or don\'t reject the null hypoth

Question

option for (b): more lor less than 0.05, reject or don't reject the null hypothesis, doesn't have any impact or could be reduce or could increase the customers' waiting time

Before Training After Training 7.44 2.32 5.84 3.30 4.73 5.91 4.22 1.49 4.83 4.35 6.07 7.59 6.05 8.41 4.64 8.40 1.30 7.01 2.40 1.51 6.12 4.71 8.53 5.95 6.50 4.86 6.47 2.77 4.58 5.53 5.36 6.68 3.40 6.21 7.73 4.67 4.08 4.25 4.98 2.46 5.39 3.45 0.85 2.08 5.32 8.16 5.66 7.75 7.01 8.23 5.67 6.87 7.84 5.13 2.37 8.51 5.63 1.77 6.77 6.08 3.79 6.06 4.86 4.04 5.70 6.41 2.16 4.14 2.82 3.19 10.33 4.84 4.11 8.79 4.17 6.41 2.49 8.67 6.75 6.05 7.29 4.88 4.05 5.08 7.00 5.57 4.80 7.32 6.52 1.04 4.09 1.01 7.22 7.59 4.68 2.76 7.23 1.40 7.09 2.49 5.24 3.72 4.30 3.87 7.43 7.90 6.81 2.25 6.55 8.12 5.66 3.01 4.74 7.07 1.84 2.08 9.93 7.44 8.77 4.38 8.14 1.91 7.42 6.09 10.27 1.83 5.69 5.95 5.20 7.15 7.74 4.09 5.82 3.92 6.36 3.56 2.31 2.01 5.49 2.20 6.93 8.02 4.38 4.38 3.34 6.84 9.09 1.96 7.66 1.75 7.53 8.94 7.49 5.84 4.73 1.20 7.49 8.33 3.50 5.22 5.81 2.06 4.44 5.98 7.16 7.95 6.33 5.69 8.22 7.04 6.79 6.73 4.88 6.20 7.64 2.89 6.88 3.22 7.13 3.95 10.42 2.05 3.98 2.56 1.98 1.48 6.70 4.65 3.89 3.46 4.52 1.71 12.34 7.99 6.36 2.83 6.16 3.05 5.17 6.79 As a follow up to the customer waiting time stuay the head of Human Resource Department has convinced the bank manager that the further training could improe the outcome He has implemented the training in Branch B and then has esked for a sample stud i at the 5% evel ofsign cance, the aining has m ro ed the cper tion, then he win vest in u her a ning Based on the sample study should he manager ask the HR o epeat trainin tor all branches? Click here for the Excel Data ile (Use Training Impact Sheet) (al Set uo the null and altemative hypothecses needed to determine whetherthe training will rcduce customer wait ng time. 110-Ugef retraining ? aiter training (Cick to select), 0, and H1. before training ?after traing (Click to select (b) Since the p-value is 4 decimal places.) which is 0 05, we the nul hypothesis. There seem to be evidence that training Click to select) the customers' waiting time. (Round your p-value answer to Click to select Click to select, c) what is the 95% Confidence Interval between the mean difference between the customer waiting time before and after traning. (Round your answer to 2 decimal places.) (d) What is the 90% Confidence Interval between the mean difference between the customer waiting time before and aftertraining Round your answer to 2 decimal places.)

Explanation / Answer

part a)

let x : before training and y : after training

H_0: mu_x =mu_y vs H_a:mu_x not equal to mu_y

part b)

x=c(7.44,5.84,4.73,4.22,4.83,6.07,6.05,4.64,1.30,2.40,6.12,8.53,6.50,6.47,4.58,5.36,3.40,7.73,4.08,4.98,5.39,0.85,5.32,5.66,7.01,5.67,7.84,2.37,5.63,6.77,3.79,4.86,5.70,2.16,2.82,10.33,4.11,4.17,2.49,6.75,7.29,4.05,7.00,4.80,6.52,4.09,7.22,4.68,7.23,7.09,5.24,4.30,7.43,6.81,6.55,5.66,4.74,1.84,9.93,8.77,8.14,7.42,10.27,5.69,5.20,7.74,5.82,6.36,2.31,5.49,6.93,4.38,3.34,9.09,7.66,7.53,7.49,4.73,7.49,3.50,5.81,4.44,7.16,6.33,8.22,6.79,4.88,7.64,6.88,7.13,10.42,3.98,1.98,6.70,3.89,4.52,12.34,6.36,6.16,5.17)

length(x)

>100

y =c(2.32,3.30,5.91, 1.49,4.35,7.59,8.41,8.40,7.01, 1.51,4.71,5.95,4.86,2.77,5.53,6.68,6.21,4.67,4.25,2.46,3.45, 2.08,8.16, 7.75,8.23,6.87,5.13,8.51, 1.77, 6.08,6.06,4.04,6.41, 4.14, 3.19,4.84,8.79, 6.41, 8.67, 6.05,4.88,5.08, 5.57, 7.32, 1.04,1.01, 7.59,2.76, 1.40, 2.49,3.72,3.87,7.90,2.25, 8.12, 3.01, 7.07, 2.08, 7.44,4.38,1.91,6.09,1.83, 5.95,7.15,4.09, 3.92, 3.56, 2.01,2.20, 8.02, 4.38, 6.84,1.96, 1.75, 8.94, 5.84, 1.20,8.33, 5.22,2.06, 5.98,7.95,5.69, 7.04, 6.73,6.20,2.89,3.22,3.95, 2.05, 2.56, 1.48,4.65,3.46,1.71, 7.99,2.83,3.05, 6.79)

length(y)

>100

t.test(x,y,var.equal = FALSE)

Welch Two Sample t-test

data: x and y

t = 3.0881, df = 195.93, p-value = 0.002307

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

0.3473506 1.5750494

sample estimates:

mean of x mean of y

5.7958 4.8346

we failed to reject Ho becuse p value >0.05

that means we are accepting Ho.

does not have any impact.

part c)

95 percent confidence interval:
0.3473506 1.5750494

part d)

90 percent confidence interval:
0.4467912 1.4756088

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