A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation. Last month the average waiting time at a bank was 8.4 minutes. The manager has installed a new computer system and claims that people will no longer have to wait as long. The hypotheses are as follows: Null hypothesis: average waiting time = 8.4 minutes Alternative hypothesis: average waiting time < 8.4 minutes Rejecting the null hypothesis means there is insufficient evidence that the mean waiting time is equal to 8.4 minutes. Accepting the null hypothesis means there is evidence to conclude that the mean waiting time is equal to 8.4 minutes. Rejecting the null hypothesis means there is evidence that the mean waiting time is not equal to 8.4 minutes. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean waiting time is less than 8.4 minutes. Rejecting the null hypothesis means there is evidence that the mean waiting time is less than 8.4 minutes. Accepting the null hypothesis means there is evidence to conclude that the mean waiting time is equal to 8.4 minutes. Rejecting the null hypothesis means there is evidence that the mean waiting time is less than 8.4 minutes. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean waiting time is less than 8.4 minutes.

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 hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the given situation.

Last month the average waiting time at a bank was 8.4 minutes. The manager has installed a new computer system and claims that people will no longer have to wait as long.
The hypotheses are as follows:
Null hypothesis: average waiting time = 8.4 minutes
Alternative hypothesis: average waiting time < 8.4 minutes

		Rejecting the null hypothesis means there is insufficient evidence that the mean waiting time is equal to 8.4 minutes. Accepting the null hypothesis means there is evidence to conclude that the mean waiting time is equal to 8.4 minutes.
		Rejecting the null hypothesis means there is evidence that the mean waiting time is not equal to 8.4 minutes. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean waiting time is less than 8.4 minutes.
		Rejecting the null hypothesis means there is evidence that the mean waiting time is less than 8.4 minutes. Accepting the null hypothesis means there is evidence to conclude that the mean waiting time is equal to 8.4 minutes.
		Rejecting the null hypothesis means there is evidence that the mean waiting time is less than 8.4 minutes. Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean waiting time is less than 8.4 minutes.

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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