The pH of a liquid is a measure of its acidity or alkalinity. Pure water was a pH of 7, which is neutral. Solutions with a pH less than 7 are acidic while solutions with a pH greater than 7 are alkaline. A biologist was interested in testing the purity of lake water in Florida. A random sample of 58 lakes was taken, and the pH of water in each lake was recorded. The sample of lakes had an average pH of 6.567 with a standard deviation of 1.861. Using a significance level of 0.01, is there evidence the mean pH of Florida lakes is not neutral? What hypotheses should be tested? Ho:μ=7Ho:μ=7 Ha:μ<7Ha:μ<7 Ho:μ≠7Ho:μ≠7 Ha:μ=7Ha:μ=7 Ho:μ=7Ho:μ=7 Ha:μ≠7Ha:μ≠7 Ho:μ=7Ho:μ=7 Ha:μ>7Ha:μ>7 αα = Test Statistic: t = (Note: round the t-score to two decimal places) probability = Select an answer 0.0818 0.0409 0.9591 decision: Select an answer Reject H₀ Fail to reject H₀ At the 0.01 level, there Select an answer is not is significant evidence to conclude the mean pH in Florida lakes is Select an answer less than greater than different than 7. Based on the decision of your test and the sample selected, what can you conclude? The mean pH of Florida lakes is neutral. The mean pH of Florida lakes is acidic. The mean pH of Florida lakes is alkaline.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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The pH of a liquid is a measure of its acidity or alkalinity. Pure water was a pH of 7, which is neutral. Solutions with a pH less than 7 are acidic while solutions with a pH greater than 7 are alkaline. A biologist was interested in testing the purity of lake water in Florida. A random sample of 58 lakes was taken, and the pH of water in each lake was recorded. The sample of lakes had an average pH of 6.567 with a standard deviation of 1.861.

Using a significance level of 0.01, is there evidence the mean pH of Florida lakes is not neutral?

What hypotheses should be tested?

Ho:μ=7Ho:μ=7
Ha:μ<7Ha:μ<7

Ho:μ≠7Ho:μ≠7
Ha:μ=7Ha:μ=7

Ho:μ=7Ho:μ=7
Ha:μ≠7Ha:μ≠7

Ho:μ=7Ho:μ=7
Ha:μ>7Ha:μ>7
αα =
Test Statistic: t = (Note: round the t-score to two decimal places)
probability = Select an answer 0.0818 0.0409 0.9591
decision: Select an answer Reject H₀ Fail to reject H₀
At the 0.01 level, there Select an answer is not is significant evidence to conclude the mean pH in Florida lakes is Select an answer less than greater than different than 7.

Based on the decision of your test and the sample selected, what can you conclude?

The mean pH of Florida lakes is neutral.
The mean pH of Florida lakes is acidic.
The mean pH of Florida lakes is alkaline.

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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