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Making use of the fact that the chi square distribution can

Making use of the fact that the chi-square distribution can be approximated with a normal distribution when v, the number of degrees of freedom, is large, show that for large samples from normal populations

Is an approximate critical region of size a for testing the null hypothesis σ2 = σ20 against the alternative σ2 > σ20 . Also construct corresponding critical regions for testing this null hypothesis against the alternatives σ2 < σ20 and σ2 ≠ σ20 (see Exercise 8θ23 on page 249).

Is an approximate critical region of size a for testing the null hypothesis σ2 = σ20 against the alternative σ2 > σ20 . Also construct corresponding critical regions for testing this null hypothesis against the alternatives σ2 < σ20 and σ2 ≠ σ20 (see Exercise 8θ23 on page 249).

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