I am having trouble with the following question in my lab report. I have turned

Question

I am having trouble with the following question in my lab report. I have turned it in numerously and still keep getting it wrong (lab TA doesn't have time to show me a correct version of the following questions.) I attached my data to this post. if you could take a screen print of F-test...etc. as well as steps on how to do it. Thanks!

1. F-test for equal variances in Soy/Adzuki seed mass data. (1 point)

2. T-test of Soy vs. Adzuki seed mass data. (1 point)

3. Statement of significance for Soy/Adzuki seed mass data. (2 points)

Red White 0.17 0.27 0.26 0.18 0.29 0.18 0.15 0.25 0.18 0.19 0.17 0.22 0.13 0.27 0.15 0.20 0.22 0.14 0.23 0.18 0.17 0.27 0.23 0.13 0.22 0.14 0.15 0.22 0.19 0.23 0.24 0.16 0.28 0.19 0.24 0.14 0.29 0.17 0.28 0.16 0.23 0.13 0.15 0.24 0.12 0.24 0.16 0.27 0.23 0.18 0.17 Average 0.27 std dev 0.023452 0.034196 Std error 0.00469 0.00684

Explanation / Answer

Answer 1) An F-test is used to test to compare two variables (variances) of the two populations. In this, we have to test variance from the first population is either greater than or less than from the variance of the second population.

In the given problem, standard variations are given therefore variances can be calculated by taking the square of them. Variance is denoted by .

Variance(red) red = (standard deviation)2
= (0.023452)2 = 0.0005499963

Variance (white) white = (standard deviation)2
= (0.034196)2 = 0.00116936641

Now, to get the F value, divide the largest variance by the smallest variance.
F value = white / red
   =   0.00116936641 / 0.0005499963
   = 2.1261

Then calculate the degrees of freedom which is equal to (N-1), where N is the sample size/number of observations
DF (red) = 25 -1 = 24 (numerator) i.e you have to see DF vertically.
DF (white) = 25-1 = 24 (denominator) i.e you have to see DF horizontally.

Compare your calculated F value with the value given in f-table of alpha value = 0.025
Generally, the alpha level value is 0.05 and for the two-tailed test (as we are comparing variances of two populations) is divided by 2. So, final alpha value = 0.025
The F-value from the f table is 2.2693 which is greater than our calculated F- value so we can accept the null hypothesis.

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