An agricultural research laboratory is evaluating two methods (Method 1, Method 2) for determining arsenic concentration in soil. Each method was tested ten times. The ten measurements associated with Method 1 yielded a sample standard deviation value of 1. (mg/kg); the ten measurements associated with Method 2 yielded a sample standard deviation value of 0.8 (mg/kg). The laboratory then conducts hypothesis-testing, at a level of significance a = 0.05, to determine the data provide sufficient evidence that Method 1 is less precise than Method 2 (a method is less precise than another if the variance from its measurements is greater than that for the other). The laboratory considers the following hypotheses: H, : o? – o = 0 versus H, : o - o > 0.

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An agricultural research laboratory is evaluating two methods (Method 1, Method 2) for
determining arsenic concentration in soil.
Each method was tested ten times.
The ten measurements associated with Method 1 yielded a sample standard deviation value of 1.2
(mg/kg); the ten measurements associated with Method 2 yielded a sample standard deviation
value of 0.8 (mg/kg).
The laboratory then conducts hypothesis-testing, at a level of significance a = 0.05, to determine if
the data provide sufficient evidence that Method 1 is less precise than Method 2 (a method is less
precise than another if the variance from its measurements is greater than that for the other).
The laboratory considers the following hypotheses: Ho: o-o 0 versus H. : o >0.
Here, o and o, denote the population variances measurements from Methods 1 and 2,
respectively.
Fill in the blanks in the following statements.
Statement
Remarks
The value of the test statistic is
Write your answer precise to two decimal
places, e.g., 8.47, 1.60, 5.92.
The relevant critical (rejection) region for the
Write your answer precise to two decimal
test is given by: [
+infinity). places, e.g., 8.47, 1.60, 5.92.
The outcome is
A. The null hypothesis is rejected; the data
provide sufficient evidence to conclude that
Write A or B.
Method 1 is less precise than Method 2.
Transcribed Image Text:An agricultural research laboratory is evaluating two methods (Method 1, Method 2) for determining arsenic concentration in soil. Each method was tested ten times. The ten measurements associated with Method 1 yielded a sample standard deviation value of 1.2 (mg/kg); the ten measurements associated with Method 2 yielded a sample standard deviation value of 0.8 (mg/kg). The laboratory then conducts hypothesis-testing, at a level of significance a = 0.05, to determine if the data provide sufficient evidence that Method 1 is less precise than Method 2 (a method is less precise than another if the variance from its measurements is greater than that for the other). The laboratory considers the following hypotheses: Ho: o-o 0 versus H. : o >0. Here, o and o, denote the population variances measurements from Methods 1 and 2, respectively. Fill in the blanks in the following statements. Statement Remarks The value of the test statistic is Write your answer precise to two decimal places, e.g., 8.47, 1.60, 5.92. The relevant critical (rejection) region for the Write your answer precise to two decimal test is given by: [ +infinity). places, e.g., 8.47, 1.60, 5.92. The outcome is A. The null hypothesis is rejected; the data provide sufficient evidence to conclude that Write A or B. Method 1 is less precise than Method 2.
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