Question

Mark all pairs of H₀/H₁ below as valid (V) or invalid (I):

1. H₀: p = 0.4 vs.   H₁: p > 0.4
2. H₀: p ≠ 0.53 vs.   H₁: p = 0.53
3. H₀: σ² = 15 vs.   H₁: σ² ≠ 15
4. H₀: µ = 3   vs.   H₁: σ² ≠ 9
5. H₀: µ = 4   vs.   H₁: µ ≠ 0.2

Answer 1

This answers your question.

Hope it helps you.

If you understood the answers please rate it positively.

Answer--->

a. Valid .because In hypothesis testing null hypothesis (H0)is always simple and alternative hypothesis(H1) is composite

b.Invalid in hypothesis testing null hypothesis(H0) is always simple but here the null hypothesis(H0) is composite that's why the b is invalid.

c.Valid.because null hypothesis(H0) is simple and alternative hypothesis (H1)is composite.

d.Invalid because in hypothesis testing we claim to test the null hypothesis(H0) against alternative hypothesis (H1)of one parameter at a time.Here in null hypothesis contain one parameter(mu) and alternative hypothesis contain another parameter (Sigma) that's why the 'b' is invalid.

e.Invalid.because Alternative hypothesis(H1) can take a value which the null hypothesis (H0) already has.Which is a contradict the assumption of hypothesis testing