A bank manager must decide whether or not to hire additional tellers. Her decision will depend partly upon how long it takes to complete customer transactions. The null hypothesis is that the mean transaction completion time, m, is at most 40 seconds. The population standard deviation is assumed to be 10 seconds. If the null is rejected, new tellers will be hired. A sample of 50 transactions was obtained with a mean of 44.5 seconds. The significance level is .05. State the Null and Alternate Hypothesis. Which test statistic does the data call for? Explain why. State Decision Rule and Critical Value. Compute the test statistic and p-value. What is your decision concerning Null? What affect would a type I (α) error have on the bank and/or customers? What affect would a type II (β) error have on the bank and/or customers?

It is given that Sample size n = 50 Sample mean = 44.5 Population SD = 10 Level of significance =…

Answered: State the Null and Alternate…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A bank manager must decide whether or not to hire additional tellers. Her decision will depend partly upon how long it takes to complete customer transactions. The null hypothesis is that the mean transaction completion time, m, is at most 40 seconds. The population standard deviation is assumed to be 10 seconds. If the null is rejected, new tellers will be hired. A sample of 50 transactions was obtained with a mean of 44.5 seconds. The significance level is .05.
1. State the Null and Alternate Hypothesis.
2. Which test statistic does the data call for? Explain why.
3. State Decision Rule and Critical Value.
4. Compute the test statistic and p-value.
5. What is your decision concerning Null?
6. What affect would a type I (α) error have on the bank and/or customers?
7. What affect would a type II (β) error have on the bank and/or customers?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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