Question

Acid rain—rain with a pH value less than 5.7, caused by the reaction of certain air pollutants with rainwater—is a growing problem in the United States. Pure rain falling through clean air registers a pH value of 5.7 (pH is a measure of acidity: 0 is acid; 14 is alkaline). A sample of n = 30 rainfalls produced pH readings with x = 3.7 and s = 0.5. Do the data provide sufficient evidence to indicate that the mean pH for rainfalls is more acidic (H_a: μ < 5.7 pH) than pure rainwater? Test using α = 0.05. Note that this inference is appropriate only for the area in which the rainwater specimens were collected.

State the null and alternative hypotheses.

H₀: μ ≠ 5.7 versus H_a: μ < 5.7H₀: μ > 5.7 versus H_a: μ < 5.7     H₀: μ = 5.7 versus H_a: μ > 5.7H₀: μ < 5.7 versus H_a: μ = 5.7H₀: μ = 5.7 versus H_a: μ < 5.7

Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

test statisticz=rejection regionz>z<

State your conclusion.

H₀ is not rejected. There is insufficient evidence to indicate that the average pH for rainfalls is more acidic than pure rainwater.H₀ is not rejected. There is sufficient evidence to indicate that the average pH for rainfalls is more acidic than pure rainwater.     H₀ is rejected. There is sufficient evidence to indicate that the average pH for rainfalls is more acidic than pure rainwater.H₀ is rejected. There is insufficient evidence to indicate that the average pH for rainfalls is more acidic than pure rainwater.

Answer 1

Null Hypothesis:

Alternate Hypothesis:

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Sample size n = 30

The sample mean = 3.7

Sample standard deviation s = 0.5

Degree of freedom df = n - 1 = 30 -1 = 29

Significance level = 0.05

Since Population sd is unknown we use one sample t-test so, test statistics is:

Rejection Region =

we can find it using excel function: =T.INV(0.05,29) = -1.7

Rejection Region > test statistics (Reject null Hypothesis)

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Conclusion: H₀ is rejected. There is sufficient evidence to indicate that the average pH for rainfalls is more acidic than pure rainwater.

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