use the given statistics to complete parts (a) and (b) assume that the populations are normally distributed (a) test whether $ \mu _ { 1 } \mu _ { 2 } $ at the $ \alpha = 0.01 $ level of significance for the given sample data (b) construct a $ 99 \% $ confidence interval about $ \mu _ { 1 } - \mu _ { 2 } $ $ h _ { 1 } \mu _ { 1 } \mu _ { 2 } $ $ \bigcirc $ b. reject $ h _ { 0 } $ there is sufficient evidence at the $ \alpha = 0.01 $ level of significance to conclude that $ \mu _ { 1 } \mu _ { 2 } $ $ \bigcirc $ c. do not reject $ h _ { 0 } $ there is sufficient evidence at the $ \alpha = 0.01 $ level of significance to conclude that $ \mu _ { 1 } \mu _ { 2 } $ $ \bigcirc $ d. do not reject $ h _ { 0 } $ there is not sufficient evidence at the $ \alpha = 0.01 $ level of significance to conclude that $ \mu _ { 1 } \mu _ { 2 } $

Question

use the given statistics to complete parts (a) and (b) assume that the populations are normally distributed (a) test whether $ \mu _ { 1 } > \mu _ { 2 } $ at the $ \alpha = 0.01 $ level of significance for the given sample data (b) construct a $ 99 \% $ confidence interval about $ \mu _ { 1 } - \mu _ { 2 } $ $ h _ { 1 } \mu _ { 1 } < \mu _ { 2 } $ $ h _ { 1 } \mu _ { 1 } = \mu _ { 2 } $ $ h _ { 1 } \mu _ { 1 } \
eq \mu _ { 2 } $ find the test statistic for this hypothesis test 0.52 (round to two decimal places as needed ) determine the p - value for this hypothesis test 0.305 (round to three decimal places as needed ) state the conclusion for this hypothesis test $ \bigcirc $ a. reject $ h _ { 0 } $ there is not sufficient evidence at the $ \alpha = 0.01 $ level of significance to conclude that $ \mu _ { 1 } > \mu _ { 2 } $ $ \bigcirc $ b. reject $ h _ { 0 } $ there is sufficient evidence at the $ \alpha = 0.01 $ level of significance to conclude that $ \mu _ { 1 } > \mu _ { 2 } $ $ \bigcirc $ c. do not reject $ h _ { 0 } $ there is sufficient evidence at the $ \alpha = 0.01 $ level of significance to conclude that $ \mu _ { 1 } > \mu _ { 2 } $ $ \bigcirc $ d. do not reject $ h _ { 0 } $ there is not sufficient evidence at the $ \alpha = 0.01 $ level of significance to conclude that $ \mu _ { 1 } > \mu _ { 2 } $

Accepted Answer

# Explanation:
## Step1: Hypothesis testing rule
If $P - value\gt\alpha$, do not reject $H_0$. Here $\alpha = 0.01$ and $P - value=0.305$.
## Step2: Compare $P - value$ and $\alpha$
Since $0.305>0.01$ (i.e., $P - value>\alpha$).

# Answer:
D. Do not reject $H_0$. There is not sufficient evidence at the $\alpha = 0.01$ level of significance to conclude that $\mu_1>\mu_2$

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QUESTION IMAGE

Question

Explanation:

Step1: Hypothesis testing rule

Step2: Compare \(P - value\) and \(\alpha\)

Answer: