Answered: Determine which type of hypothesis test…

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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Determine which type of hypothesis test is appropriate (if any) in each situation. Type 1: test a population mean, population standard deviation is known Type 2: test a population mean, population standard deviation is unknown Type 3: test a population proportion Then Clearly state the null and alternative hypothesis. Then, compute the test statistic, and determine the conclusion of the test. (You may compute a p-value or use critical values to determine the conclusion of the test) The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.05 level that the medicine relieves pain in more than 320 seconds. For a sample of 32 patients, the mean time in which the medicine relieved pain was 325 seconds. Assume the population standard deviation is 23. Make the decision to reject or fail to reject the null hypothesis

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 + ...

Expert Solution

Given Hypotheses

$T h e P o p u l a t i o n m e a n : μ = 320 s e c o n d s a n d P o p u l a t i o n S \tan d a r d D e v i a t i o n : σ = 23 s e c o n d s F r o m t h e s a m p l e, S a m p l e s i z e : n = 32 S a m p l e m e a n : \bar{x} = 325 s e c o n d s$

$T o t e s t : H_{0} : μ = 320 s e c o n d s v s H_{1} : μ > 320 s e c o n d s$

Test Statistic

The test statistic is obtained as:

$z_{0} = \frac{\bar{x} - μ}{\frac{σ}{\sqrt{n}}} = 1.23$

The critical value is obtained as:

$z_{0.05} = 1.645$

$A s z_{0} = 1.23 < z_{0.05} = 1.645 w e c a n n o t r e j e c t H_{0} a t 5 % l e v e l o f s i g n i f i c a n c e$

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