9-1 a) *H*_{0} : *μ* = 25, *H*_{1}: *μ* ≠ 25 Yes, because the hypothesis is stated in terms of the parameter of interest, inequality is in the alternative hypothesis, and the value in the null and alternative hypotheses matches.

b) *H*_{0} : *σ* > 10, *H*_{1} : *σ* = 10 No, because the inequality is in the null hypothesis.

c) No, because the hypothesis is stated in terms of the statistic rather than the parameter.

d) *H*_{0} : *p* = 0.1, *H*_{1} : *p* = 0.3 No, the values in the null and alternative hypotheses do not match and both of the hypotheses are equality statements.

e) *H*_{0} : *s* = 30, *H*_{1} : *s* > 30 No, because the hypothesis is stated in terms of the statistic rather than the parameter.

9-3 a) *H*_{0} : *σ* = 20*nm*, *H*_{1} : *σ* < 20*nm*

b) This result does not provide strong evidence that the standard deviation has not been reduced. There is insufficient evidence to reject the null hypothesis, but this is not strong support for the null hypothesis.

9-5 a) *α* = P(reject H_{0} when H_{0} is true)

The probability of rejecting the null hypothesis when it is true is 0.02275.

b) The probability of accepting the null hypothesis when it is false is 0.15866.

c) β = P(accept H_{0} when μ = 11.25) ...

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