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# 統計問題請教統計高手>< 麻煩了!!

A random sample of seven measurement gave X(平均數)=9.4,s^2=1.84.

a. What assumptions must you make concerning the population in order to test a hypothesis about σ^2 ?

b.Suppose the assumption in part a are statics.Test the null hypothesis σ^2 =1 against the alternative hypothesis σ^2 >1.Use α=.05.

c.Test the null hypothesis σ^2 = 1 against the alternative hypothesis σ^2≠1.Use α =.05.

20點!

### 1 個解答

• 1 0 年前
最佳解答

(a) The population follows normal distribution. The variances of the populations to be compared are equal

(b) H_0 : σ^2 = 1

H_1 : σ^2 > 1

α = 0.05, critical value: Χ_6(0.05) = 12.6

Test - statistic = (n - 1)S^2/σ^2 = 10.8 < 12.6

Conclusion: Do not reject H_0.

(c) H_0 : σ^2 = 1

H_1 : σ^2 > 1

α = 0.05, critical value: Χ_6(0.025) = 14.4, Χ_6(0.975) = 1.237

Test - statistic = (n - 1)S^2/σ^2 = 10.8

Since 1.237 < 10.8 < 14.4

Conclusion: Do not reject H_0.

2011-03-27 10:12:52 補充：

(c) H1: σ^2≠1