Emissions of sulfur dioxide by industry set off chemical changes in the atmosphe

Question

Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in "acid rain." The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0. Suppose that pH measurements of rainfall on different days in a Canadian forest follow a Normal distribution with standard deviation = 0.5. Is this good evidence that the mean pH for all rainy days is less than 5.0? Find the P-value in each of the following situations. (Use 2 decimal places for z-values and 4 decimal places for p-values.)

(a) We measure the acidity of rainfall on 4 days. The average pH is x = 4.7.

(b) Use a larger sample of 16 days. The average pH is x = 4.7.

(c) Finally, measure acidity for a sample of 37 days. The average pH is x = 4.7.

Explanation / Answer

Here H0: mu=5 vs H1: mu<5

a. z=xbar-mu/(sd/sqrt(n))=(4.7-5)/(0.5/2)=-1.2

The P-Value is 0.11507.

The result is not significant at p < 0.05.

b. Using same formula of a we get z=-2.4

The P-Value is 0.008198.

The result is significant at p < 0.05.

c. here z=-3.65

The P-Value is 0.000131.

The result is significant at p < 0.05.

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