Question

Soil acidity is measured by a quantity called pH. A scientist wants to estimate

the difference in the average pH for two large fields using pH measurements from

randomly selected core samples. If the scientist selects 20 core samples from field I

and 15 core samples from field 2, independently of each other, find the approximate

probability that the sample mean of the 40 pH measurements for field 1 will be

larger than that for field 2 by at least 0.5.The sample variances for pH measure-

ments for fields I and II are 1 and 0.8, respectively. In the past, both fields have

shown approximately the same mean soil acidity levels. Suppose the populations

of the measurements are normally distributed.

Answer 1

Field 1

Sample Size (n1) = 20

Variance = 1

Std Dev (s1) = sqrt(1) = 1

Field 2

Sample Size (n2) = 15

Variance = 0.8

Std Dev (s2) = sqrt(0.8) = 0.894

Given,

X1-X2 = 0.5

Alpha = 0.05

Null and Alternate Hypothesis

H0: µ1 = µ2

Ha: µ1 > µ2

Test Statistic

Assuming, the population std deviation is not same.

t = (X1 ­­­– X2 ­– (µ1 - µ2))/ (s12/n1 + s22/n2 )1/2 = 1.56

p-value = TDIST(1.56,20+15-2,1) = 0.064692

Result

Since the p-value is greater than 0.05, we fail to reject the null hypothesis.

Approx Probability = 0.065

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