Question

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 59 lakes was taken, and the pH of water in each lake was recorded. The sample of lakes had an average pH of 6.729 with a standard deviation of 1.827.   

Using a significance level of 0.10, 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 0.8704 0.1296 0.2592   
• decision: Select an answer Reject H₀ Fail to reject H₀
• At the 0.10 level, there Select an answer is not is   significant evidence to conclude the mean pH in Florida lakes is Select an answer different than greater than less 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.

Answer 1

Let denotes the mean pH of Florida lakes.

There is not significant evidence to conclude the mean pH in Florida lakes is different than 7.

The mean pH of Florida lakes is neutral.