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A new purification unit is installed in a chemical process. Before its installation, a random sample yielded the following data about the percentage of impurity: x1 = 9.85 , S12 = 81.73 , and n1 = 8 . After installation, a random sample resulted in x2 = 8.08 , S2 = 78.46 , and n2 = 10 .

A new purification unit is installed in a chemical process. Before its installation, a random sample yielded the following data about the percentage of impurity: x1 = 9.85 , S12 = 81.73 , and n1 = 8 . After installation, a random sample resulted in x2 = 8.08 , S2 = 78.46 , and n2 = 10 .

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 11PPS
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A new purification unit is installed in a chemical process. Before its installation, a random sample yielded the following data about the percentage of impurity: x1 = 9.85 , S12 = 81.73 , and n1 = 8 . After installation, a random sample resulted in x2 = 8.08 , S2 = 78.46 , and n2 = 10 .
b) Can you conclude that the new purification device has reduced the mean percentage of impurity? Use a = 0.05. Suppose the two unknown variances are equal. (i) What will be your null and alternative hypothesis? (ii) When will you reject the null hypothesis Ho in terms of to (and tan₁+n₂-2, ₁-an₁+n₂-2, ta/2n₁+n₂-2 and/or t₁-a/2.n₁+n₂-2)? (iii) What is the value of tan,+n₂-2? (iv) What is the value of to? (v) Based on (ii)-(iv), your decision on H, would be: (vi) Which is true?: (v) means "The mean impurity before and after are:" (the same) or (not the same)?
Transcribed Image Text:b) Can you conclude that the new purification device has reduced the mean percentage of impurity? Use a = 0.05. Suppose the two unknown variances are equal. (i) What will be your null and alternative hypothesis? (ii) When will you reject the null hypothesis Ho in terms of to (and tan₁+n₂-2, ₁-an₁+n₂-2, ta/2n₁+n₂-2 and/or t₁-a/2.n₁+n₂-2)? (iii) What is the value of tan,+n₂-2? (iv) What is the value of to? (v) Based on (ii)-(iv), your decision on H, would be: (vi) Which is true?: (v) means "The mean impurity before and after are:" (the same) or (not the same)?
Q2. A new purification unit is installed in a chemical process. Before its installation, a random sample yielded the following data about the percentage of impurity: x₁=9.85, S3=81.73, and n₁ = 8. After installation, a random sample resulted in ₂8.08, S3 = 78.46, and n₂ =10. a) Can you conclude that the two variances are equal? Use a = 0.05. (i) What will be your null and alternative hypothesis? (ii) To test the hypothesis, you will Reject Ho if Fo> Fa/2n₁-1,2-1 or Fo < F₁-a/2,n₁-1,n₂-1″ What is the value of Fa/2,₁-1,2-1? (iii) What is the value of F₁-a/2,₁-1,2-1? (iv) What is the value of Fo? (v) Based on (ii)-(iv), your decision on H, would be: (vi) Which is true?: (v) means "The impurity variances before and after are:" (the same) or (not the same)?
Transcribed Image Text:Q2. A new purification unit is installed in a chemical process. Before its installation, a random sample yielded the following data about the percentage of impurity: x₁=9.85, S3=81.73, and n₁ = 8. After installation, a random sample resulted in ₂8.08, S3 = 78.46, and n₂ =10. a) Can you conclude that the two variances are equal? Use a = 0.05. (i) What will be your null and alternative hypothesis? (ii) To test the hypothesis, you will Reject Ho if Fo> Fa/2n₁-1,2-1 or Fo < F₁-a/2,n₁-1,n₂-1″ What is the value of Fa/2,₁-1,2-1? (iii) What is the value of F₁-a/2,₁-1,2-1? (iv) What is the value of Fo? (v) Based on (ii)-(iv), your decision on H, would be: (vi) Which is true?: (v) means "The impurity variances before and after are:" (the same) or (not the same)?
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