$ \mathrm{H}_{\mathrm{a}}: \mu21.1, \bar{x}=21.5, \sigma=6, \mathrm{n}=100 $; Without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.
A) $ \mathrm{H}_{\mathrm{a}} $ is supported; $ \bar{x} $ is less than 1 standard deviation above the claimed mean.
B) $ \mathrm{H}_{\mathrm{a}} $ is supported; $ \bar{x} $ is more than 4 standard deviations above the claimed mean.
C) $ \mathrm{H}_{\mathrm{a}} $ is not supported; $ \bar{x} $ is less than 1 standard deviation above the claimed mean.
D) $ \mathrm{H}_{8} $ is not supported; $ \bar{x} $ is more than 4 standard deviations above the claimed mean.

Question

$ \mathrm{H}_{\mathrm{a}}: \mu>21.1, \bar{x}=21.5, \sigma=6, \mathrm{n}=100 $; Without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.
A) $ \mathrm{H}_{\mathrm{a}} $ is supported; $ \bar{x} $ is less than 1 standard deviation above the claimed mean.
B) $ \mathrm{H}_{\mathrm{a}} $ is supported; $ \bar{x} $ is more than 4 standard deviations above the claimed mean.
C) $ \mathrm{H}_{\mathrm{a}} $ is not supported; $ \bar{x} $ is less than 1 standard deviation above the claimed mean.
D) $ \mathrm{H}_{8} $ is not supported; $ \bar{x} $ is more than 4 standard deviations above the claimed mean.

Quizplus · Accepted Answer

The sample mean $\bar{x}$ is only 0.4 standard deviations above the claimed mean, which is not enough to support the alternate hypothesis.

Ha:μ>21.1,xˉ=21.5,σ=6,n=100 \mathrm{H}_{\mathrm{a}}: \mu>21.1, \bar{x}=21.5, \sigma=6, \mathrm{n}=100 Ha​:μ>21.1,xˉ=21.5,σ=6,n=100 ; Without Computing a P-Value, Determine Whether the Alternate Hypothesis

$\mathrm{H}_{\mathrm{a}}: \mu>21.1, \bar{x}=21.5, \sigma=6, \mathrm{n}=100$ ; Without Computing a P-Value, Determine Whether the Alternate Hypothesis