Test the hypothesis (using z-test) of each of the following situations. Show complete steps. An environmentalist collects a liter of water from 45 different locations along the banks of a stream. He measures the amount of dissolved oxygen in each specimen. The mean oxygen level is 4.62 mg, with an overall standard deviation of 0.92. A water purifying company claims that the mean level of oxygen in the water is 5 mg. Conduct a hypothesis test with = 0.001 to determine whether the mean oxygen level is less than 5 mg. (follow these steps) Step1: Formulate the null and the alternative hypothesis. Step2: Specify the level of significance and decide whether a one-tailed test (left or right-tailed) or a two-tailed test shall be used. Step3: Decide the test statistic to be used such as (z-test, t-test, chi-squared, or F). Find the critical or tabular value. Step4: Compute for the value of the test statistic using the data from the population and the sample/s. Step5: Make a decision. a. If the computed value of the test statistic is greater than the critical or tabular value, reject the null hypothesis and accept the alternative hypothesis. b. If the computed value of the test statistic is less than the critical or tabular value, accept the null hypothesis and reject the alternative hypothesis. Step 6: State the conclusion.

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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Test the hypothesis (using z-test) of each of the following situations. Show complete steps.

An environmentalist collects a liter of water from 45 different locations along the banks of a stream. He measures the amount of dissolved oxygen in each specimen. The mean oxygen level is 4.62 mg, with an overall standard deviation of 0.92. A water purifying company claims that the mean level of oxygen in the water is 5 mg. Conduct a hypothesis test with = 0.001 to determine whether the mean oxygen level is less than 5 mg.

(follow these steps)

Step1: Formulate the null and the alternative hypothesis.

Step2: Specify the level of significance and decide whether a one-tailed test (left or right-tailed) or a two-tailed test shall be used.

Step3: Decide the test statistic to be used such as (z-test, t-test, chi-squared, or F). Find the critical or tabular value.

Step4: Compute for the value of the test statistic using the data from the population and the sample/s.

Step5: Make a decision.

a. If the computed value of the test statistic is greater than the critical or tabular value, reject the null hypothesis and accept the alternative hypothesis.

b. If the computed value of the test statistic is less than the critical or tabular value, accept the null hypothesis and reject the alternative hypothesis.

Step 6: State the conclusion.

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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