5. (a) Two samples of size 9 and 8 give the sum ofsquares of deviations from their respectivemeans equal 160 inches and 91 inches squarerespectively. Can they be regarded as drawnfrom two normal populations with the samevariance ?03!(F for 8 and 7 d. f. = 3.73).
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Answer:
5. (a) Two samples of size 9 and 8 give the sum ofsquares of deviations from their respectivemeans equal 160 inches and 91 inches squarerespectively. Can they be regarded as drawnfrom two normal populations with the samevariance ?03!(F for 8 and 7 d. f. = 3.73).
Answer: Yes they can be regarded as drawn from the same population.
Step-by-step explanation: H0: σX2 = σY2 is the null hypothesis.
That is, the two population variances do not significantly differ from one another.
H1: σX2 ≠ σY2 is an alternate hypothesis.
That is, there is a big disparity between the variances of the two populations.
Data in Step 2
∑ ( x-x° )² =160 and ∑( y-y°)²=91
m = 9, n = 8
Step 3: Significance Level
α = 10%
Test Statistic in Step Four :
F =s1²/s2² =20/13= 1.54 .
Since H1 is a two-sided alternative hypothesis the corresponding critical values are: 3.73 and 2.86.
Since f (8, 7),0.95 = 0.286 < F0 = 1.54 < f (8, 7),0.05 = 3.73, the null hypothesis is not rejected and we conclude that there is no significant difference between the two population variances.