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STA643 - Experimental Designs

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    Q. 1

    Varieties A B C 23 18 16 26 28 25 20 17 12 17 21 14

    Test the hypothesis that the three verities of potatoes are not different in the yielding capabilities.

    Solution Q.1:

    eab1da79-9b7d-4209-bc9c-5e3576e8addc-image.png 4961a077-5945-4b8e-b23c-6d582c865b5c-image.png 1310afa9-18b5-4334-b378-db2070054979-image.png a4badf0e-24fa-4a44-91f7-ec8276f9e5aa-image.png

    Q.2 Solution:

    Complete the ANOVA table.

    Source of variation Sum of squares Degrees of freedom Mean square F B/W treatments 79.44 4 19.860 6.90 Error 57.600 20 2.88 Total 137.040 24
  • STA643 Assignment 1 Solution and Discussion

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    Solution:
    Question no. 1:
    Test the hypothesis that the mean of a normal population with known variance 70 is 31, if a sample of size 13 gave x ̅ = 34. Let the alternative hypothesis be H1: µ > 31, and let α = 0.10.
    Solution:
    Formulation of Hypothesis:
    Ho: µ = 31
    H1: µ > 31
    Level of Significance:
    α = 0.10
    Test Statistics:
    z=(x ̅-μ)/(σ⁄√n)
    Calculation:
    z=(34-31)/(√70⁄√13)

    z = 1.29.
    Critical Region:
    Reject Ho, if
    Z > Zα
    1.29 > Z0.10
    1.29 > 1.28
    We reject Ho.
    Conclusion:
    Since 1.29 > 1.28 fall in the critical region, so we reject Ho.
    Questions no. 2:
    Explain in detail why it is not a good statistical procedure to perform several t-test on pairs of means , when several means are to be compared. Suggest the alternative statistical procedure and also give its assumptions.
    Solution:
    Whenever we compare more than two population means, we apply the two-sample t-test to all possible pairwise comparisons of means. For example, if we wish to compare 4 population means, there will be 6 pairs and to test the hypothesis that all four population means are equal, would require six two-sample t-test. This type of multiple two-sample t-test has two disadvantages. First, the procedure is difficult and time consuming and secondly, the level of significance increases as the number of t-test increases. Thus, a series of two-sample t-test is not a good procedure. ANOVA is a technique that measure the variations between the means.
    Assumptions of ANOVA:
    1: Experimental errors are normally distributed.
    2: Equal variance between the treatments.
    3: Samples are independent.