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 p.m. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes 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 and stored in Bank1 . These data are: 4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20 4.50 6.10 0.38 5.12 6.46 6.19 3.79 Suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 p.m. lunch period. Data are collected from a random sam- ple of 15 customers and stored in Bank2 . These data are: 9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35 10.49 6.68 5.64 4.08 6.17 9.91 5.47 A.) Assuming that the population variances from both banks are equal, is there evidence of a difference in the mean waiting time between the two 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)? D.) Construct and interpret a 95% confidence interval estimate of the difference between the population means in the two branches. E.) Repeat (a), assuming that the population variances in the two branches are not equal. Compare these results with those of Problem 10.12 (a).
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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 p.m. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes 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 and stored in Bank1 . These data are:
4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20 4.50 6.10 0.38 5.12 6.46 6.19 3.79
Suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 p.m. lunch period. Data are collected from a random sam- ple of 15 customers and stored in Bank2 . These data are:
9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35 10.49 6.68 5.64 4.08 6.17 9.91 5.47
A.) Assuming that the population variances from both banks are equal, is there evidence of a difference in the mean waiting time between the two 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)?
D.) Construct and interpret a 95% confidence
E.) Repeat (a), assuming that the population variances in the two branches are not equal. Compare these results with those of Problem 10.12 (a).
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