### Design and analysis of completely randomized design

Assignment Help Basic Statistics
##### Reference no: EM13869958

Design and Analysis of Completely Randomized Design

I.  Objectives:

At the end of the exercise, the student should be able to:

a. Identify the treatment, experimental units and response variable of an experiment laid in CRD;

b. State the linear model and define each component in terms of the given problem;

c. Analyze and interpret data from an experiment laid out in CRD; and

d. Implement appropriate analysis for CRD using SAS.

II. Methods:

PART A:

The leaves of certain plants in the genus Albizzia will fold and unfold in response to various light conditions. We have taken 15 different leaves and subjected them to red light such that all 15 leaves began to receive red light exactly at the same time and the red light was removed after 3 minutes. The amount of red light was held constant and equal across all leaves. After 3 minutes, the leaves were divided into three groups of five at random. The leaflet angles were then measured 30, 45 and 60 minutes after light exposure. Other than time elapsed from light exposure to leaflet angle measurement, the leaves were treated identically. The objective of the experiment is to test the hypothesis that time elapsed from exposure to measurement does not affect leaflet angle. Mean results from preliminary computations were 139.6 for 30, 113.6 for 45 and 122.4 for 60. Moreover, sum of squares for experimental error was 9417.6.

1. Specify the treatment, experimental unit and response variable for this experiment.

2. What are the sources of variation in this experiment laid out in CRD?

3. Perform a possible randomization to allocate 5 leaves each to the treatment levels;

 SV df SS MS Fc F-tab Decision Total

4. Given results from preliminary computations, construct the ANOVA table using the format below.

PART B:

Scientists are interested in whether energy costs involved in reproduction affect longevity. In this experiment, 125 male fruit flies were grouped at random into five sets of 25. In one group, the males were kept by themselves. In two groups, the males were supplied with one or eight receptive virgin female fruit flies per day. In the other two groups, the males were supplied with one or eight unreceptive (pregnant) female fruit flies per day. The longevity of the flies (in days) was observed. Analyze the data shown below to test the null hypothesis that reproductive activity does not affect longevity.

 Companion Longevity (days) none 35 37 49 46 63 39 46 56 63 65 56 65 70 63 65 70 77 81 86 70 70 77 77 81 77 1 pregnant 40 37 44 47 47 47 68 47 54 61 71 75 89 58 59 62 79 96 58 62 70 72 75 96 75 1 virgin 46 42 65 46 58 42 48 58 50 80 63 65 70 70 72 97 46 56 70 70 72 76 90 76 92 8 pregnant 21 40 44 54 36 40 56 60 48 53 60 60 65 68 60 81 81 48 48 56 68 75 81 48 68 8 virgin 16 19 19 32 33 33 30 42 42 33 26 30 40 54 34 34 47 47 42 47 54 54 56 60 44

Conduct a complete test of hypothesis (Ho and Ha, test procedure, test statistics, decision rule, ANOVA table from SAS output, decision and conclusion)

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