Instructor-created question Question Help A bank with branches located in a comm
ID: 3327145 • Letter: I
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Instructor-created question Question Help A bank with branches located in a commercial district of a city and in a residential district 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 time that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers at each branch Click here to view the bank branch data a. Assuming that the population variances from both banks are not equal, is there evidence of a difference in the mean waiting time between the two branches? (Use =0.1 be the mean waiting time of the commercial district branch and 2 be the mean waiting time of the residential district branch. Choose Determine the hypotheses. Let the correct answer below 3 Determine the p-value in (a) and interpret its meaning p-value-Round to six decimal places as needed.) Choose the correct conclusion below A. Do not reject Ho. There is insufficient evidence that the means differ ( B. Reject Ho-There is sufficient evidence that the means differ ° C. Do not reject Ho . There is sufficient evidence that the means differ 0 D. Reject Ho-There is insufficient evidence that the means differ Which of the following is the correct interpretation of the p-value? The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the of the two offices b. In addition to unequal variances, what assumption is necessary in (a)? 0 A. Since the sample sizes are both less than 30, it must be assumed that the sample variances are equal O B. Since the sample sizes are both less than 30, it must be assumed that both sampled populations are approximately normal ° C. Since the sample sizes are both less than 30, it must be assumed that the samples are specifically chosen and not independently sampled D. Since the sample sizes are both less than 30, it must be assumed that the sample sizes are equalExplanation / Answer
a.
The correct option is D.
H0: 1 = 2
H1: 1 2
The mean of wait imes from the commercial district branch is 4.283333
The mean of wait imes from the residential district branch is 7.172
The standard deviation of wait imes from the commercial district branch is s1 = 1.599454
The standard deviation of wait imes from the residential district branch is s2 = 2.107928
The standard error (SE) of the sampling distribution.
SE = sqrt[ (s12/n1) + (s22/n2) ]
SE = sqrt[ (1.5994542/15) + (2.1079282/15) ] = 0.6832088
The degrees of freedom (DF) is:
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
DF = (1.5994542/15 + 2.1079282/15)2 / { [ (1.5994542 / 15)2 / (15 - 1) ] + [ (2.1079282 / 15)2 / (15 - 1) ] }
= 26 (Rounding to nearest integer)
Test statistic, t = Difference in means / SE
= (7.172 - 4.283333) / 0.6832088 = 4.228088
P[t > 4.228088] for df = 26 is 0.0001286779
As, it is two tail test, p-value = 2 * P[t > 4.228088] = 2 * 0.0001286779 = 0.000257
As, p-value is less than significance level of 0.1, the correct option is,
B. Reject H0. There is sufficient evidence that the means differ.
The p-value is the probability of getting a test statistic equal or more extreme than the sample result if there is no difference in mean waiting time of two offices.
b.
B. Since the sample sizes are both less than 30, it must be assumed that both sampled populations are approximately normal.
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