For the following pairs of assertions, indicate which do not comply with our rules for setting up hypotheses and why (the subscripts 1 and 2 differentiate between quantities for two different populations or samples):

(a) H0: μ = 100, Ha: μ > 100 These hypotheses comply with our rules. H0 cannot include equality, so these hypotheses are not in compliance. Each μ is a statistic, so these hypotheses do not comply with our rules. The asserted value in H0 should not appear in Ha, so these hypotheses are not in compliance.

(b) H0: σ = 20, Ha: σ ≤ 20 These hypotheses comply with our rules. Ha cannot include equality, so these hypotheses are not in compliance. Each σ is a statistic, so these hypotheses do not comply with our rules. The asserted value in H0 should not appear in Ha, so these hypotheses are not in compliance.

(c) H0: p ≠ 0.25, Ha: p = 0.25 These hypotheses comply with our rules. Ha cannot include equality, so these hypotheses are not in compliance. Each p is a statistic, so these hypotheses do not comply with our rules. The asserted value in H0 should not appear in Ha, so these hypotheses are not in compliance.

(d) H0: μ1 − μ2 = 25, Ha: μ1 − μ2 > 100 These hypotheses comply with our rules. H0 cannot include equality, so these hypotheses are not in compliance. Each μ is a statistic, so these hypotheses do not comply with our rules. The asserted value in H0 should also appear in Ha, so these hypotheses are not in compliance.

(e) H0: S12 = S22, Ha: S12 ≠ S22 These hypotheses comply with our rules. H0 cannot include equality, so these hypotheses are not in compliance. Each S is a statistic, so these hypotheses do not comply with our rules. The asserted value in H0 should not appear in Ha, so these hypotheses are not in compliance.

(f) H0: μ = 120, Ha: μ = 150 These hypotheses comply with our rules. Ha cannot include equality, so these hypotheses are not in compliance. Each μ is a statistic, so these hypotheses do not comply with our rules. If μ appears in H0, then it should not appear in Ha, so these hypotheses are not in compliance.

(g) H0: σ1/σ2 = 1, Ha: σ1/σ2 ≠ 1 These hypotheses comply with our rules. H0 cannot include equality, so these hypotheses are not in compliance. Each σ is a statistic, so these hypotheses do not comply with our rules. The asserted value in H0 should not appear in Ha, so these hypotheses are not in compliance.

(h) H0: p1 − p2 = −0.1, Ha: p1 − p2 < −0.1 These hypotheses comply with our rules. H0 cannot include equality, so these hypotheses are not in compliance. Each p is a statistic, so these hypotheses do not comply with our rules. The asserted value in H0 should not appear in Ha, so these hypotheses are not in compliance.