a bank is studying the average time that it takes 6 of its tellers to serve a customer. Customers line up in the queue and are served by the next available teller. Based on service time for the last 140 customers, the following ANOVA result is obtained.A bank branch manager wondered if the average service times among the tellers are different. Source df ss ms f p-value teller 5 3315.32 663.064 1.508 0.1914 error 134 58919.1 439.695 total 139 62234.4 a. What is the null hypothesis: at least two of the means are different or $u_1=u_2=...=u_6$ b.at the 10% significance level do we reject the null hypothesis or cannot reject the null hypothesis
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This can be written as $H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4 = \mu_5 = \mu_6$, where $\mu_i$ represents the average service time for teller $i$. Show more…
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Question 1 From time to time, unknown to its employees, the research department at Post Bank observes various employees for their work productivity. Recently this department wanted to check whether the four tellers at a branch of this bank serve, on average, the same number of customers per hour. The research manager observed each of the four tellers for a certain number of hours. The Table 1 gives the number of customer served by the four tellers during each of the observed hours. Table 1 Teller A Teller B Teller C 19 14 11 21 16 14 26 14 21 24 13 13 18 17 16 13 18 At the 1% significance level, test the null hypothesis that the mean number of customers served per hour by each of these four tellers is the same. Assume that all the assumptions required to apply the one-way ANOVA procedure hold true. State the appropriate null and alternative hypothesis for the above test.
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Question 1 From time to time, unknown to its employees, the research department at Post Bank observes various employees for their work productivity. Recently this department wanted to check whether the four tellers at a branch of this bank serve, on average, the same number of customers per hour. The research manager observed each of the four tellers for a certain number of hours. The Table 1 gives the number of customer served by the four tellers during each of the observed hours. Table 1 Teller A Teller B Teller C 19 14 11 21 16 14 26 14 21 24 13 13 18 17 16 13 18 At the 1% significance level, test the null hypothesis that the mean number of customers served per hour by each of these four tellers is the same. Assume that all the assumptions required to apply the one-way ANOVA procedure hold true. Complete the ANOVA table in Table 2. (6 marks) Table 2: ANOVA Table Source SS df MS F Treatment 156.7412 (ii) (iv) (vi) Error (i) (iii) (v) Total 280.9412 16 b.From answer (c), make a decision.
A bank is studying the time that it takes 6 of its tellers to serve an average customer. Customers wait in line and then go to the next available teller. The boxplot for the last 140 customers and the times it took each teller is to the right. Complete parts a through c. Source DF Sum of Squares Mean Square F-ratio P-value Teller 5 7607.20 1521.439 3.460 0.0057 Error 134 58919.1 439.695 Total 139 66526.3 a) What are the null and alternative hypotheses? A. H0: μ1 = μ2 = μ3 = μ4 = μ5 = μ6 HA: μ1 < μ2 and μ2 > μ3 B. H0: μ1 = μ2 = μ3 = μ4 = μ5 = μ6 HA: not all means are equal C. H0: μ2 = μ3 HA: μ2 > μ3 D. H0: μ2 > μ3 HA: μ2 = μ3 E. H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 ≠ μ6 HA: μ1 = μ2 = μ3 = μ4 = μ5 = μ6 F. H0: μ1 < μ2 and μ2 > μ3 HA: μ1 = μ2 = μ3 = μ4 = μ5 = μ6
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