12. Find the rejection region for the hypothesis test based on the information given. The population is normally distributed H? ?=27 Ha ?<27 ?=0.05 , n=12, ?=2.2 a. z?-1.645 b. t?-1.645 c. z?1.645 d. t?1.795 e. t?-1.795
Added by Timothy A.
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Step 1
First, we need to determine the test statistic to use. Since the population is normally distributed and the sample size is small (n=12), we will use the t-test statistic. Show more…
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4. Find the rejection region (for the standardized test statistic) for each hypothesis test based on the information given. The population is normally distributed. Identify the test as left-tailed, right-tailed, or two-tailed. a. H0 : μ = −61 vs. Ha : μ ≠ −61 @ α = 0.005, n = 8, σ unknown. b. H0 : μ = 73 vs. Ha : μ > 73 @ α = 0.001, n = 22, σ unknown. c. H0 : μ = 1134 vs. Ha : μ < 1134 @ α = 0.001, n = 21, σ unknown. d. H0 : μ = 0.13 vs. Ha : μ ≠ 0.13 @ α = 0.001, n = 14, σ = 0.026.
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Find the rejection region (for the standardized test statistic) for each hypothesis test based on the information given. The population is normally distributed. a. $\boldsymbol{H}_{\mathrm{a}}: \boldsymbol{\mu}-27 \mathrm{vs} . \boldsymbol{H}_{\mathrm{a}}: \mu<27 @ \mathrm{a}-\mathrm{0.05}, n=12, \mathrm{\sigma}=2.2$. b. $\boldsymbol{H}_{\mathrm{a}}: \boldsymbol{\mu}-5 \mathrm{~s}$ vs. $\boldsymbol{H}_{a}: \boldsymbol{\mu}+52 @ \mathrm{a}-0.05, n=6, \sigma$ unknown. C. $\boldsymbol{H}_{\mathrm{a}}: \boldsymbol{\mu}=-105 \mathrm{vs} . \boldsymbol{H}_{\mathrm{a}}: \boldsymbol{\mu}>-105 @ \mathrm{a}-\mathrm{0} .10, n=24, \sigma$ unknown. d. $\boldsymbol{H}_{\mathrm{D}}: \boldsymbol{\mu}-78.8$ vs. $\boldsymbol{H}_{\mathrm{a}}: \boldsymbol{\mu}+78.8 @ \mathrm{a}-\mathrm{0} .10, \mathrm{n}=8, \sigma=1.7$
Testing Hypotheses
Small Sample Tests for a Population Mean
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