Chapter 6, Section 2-HT, Exercise 128 - MathPad Are Florida Lakes Acidic or Alkaline? The pH of a liquid is a measure of its acidity or alkalinity. Pure water has 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 basic, or alkaline. The dataset FloridaLakes gives information, including pH values, for a sample of lakes in Florida. Computer output of descriptive statistics for the pH variable is shown: Descriptive Statistics: pH Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum pH 53 0 6.591 0.177 1.288 3.600 5.800 6.800 7.450 9.100 Click here for the dataset associated with this question. Correct. (a) How many lakes are included in the dataset? What is the mean pH value? What is the standard deviation? Enter the exact answers. n= Enter your answer in accordance to item (a) of the question statement x¯= Enter your answer in accordance to item (a) of the question statement s= Enter your answer in accordance to item (a) of the question statement SHOW HINT SHOW SOLUTION SHOW ANSWER LINK TO TEXT Correct. (b) Use the descriptive statistics above to conduct a hypothesis test to determine whether there is evidence that average pH in Florida lakes is different from the neutral value of 7. State the null and alternative hypotheses. Your answer should be an expression composed of symbols: =,≠,<,>,μ,μ1,μ2,p,p1,p2,7,ρ,p^,p^1,p^2,r. H0:μ=7 vs Ha:μ≠7Edit SHOW HINT SHOW SOLUTION SHOW ANSWER LINK TO TEXT Your answer is partially correct. Try again. (c) Show all details of the test described in part (b) and use a 5% significance level. Give the test statistic and the p-value. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. test statistic = Enter your answer in accordance to item (b) of the question statement p-value = Enter your answer in accordance to item (b) of the question statement What is the conclusion? Choose the answer from the menu in accordance to item (b) of the question statement H0. If there is evidence that it is not neutral, does the mean appear to be more acidic or more alkaline? Choose the answer from the menu in accordance to item (b) of the question statement SHOW HINT LINK TO TEXT Correct. (d) Compare the test statistic and p-value you found in part (c) to the computer output below for the same data: One-Sample T: pH Test of mu =7 vs not =7 Variable N Mean StDev SE Mean 95% CI T P pH 53 6.591 1.288 0.177 (6.235,6.946) -2.31 0.025 The same up to round off error Different
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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