The null hypothesis and the alternative hypothesis are opposite in content.
The alternative hypothesis usually need to be tested.
The alternative hypothesis is supported by rejecting the null hypothesis.
The true proportion of people in that town suffering from depression or a depressive illness is not lower than the percent in the general adult American population.
The true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.
Hypotheses (null) : p = 0.095 (is always equal sign)
Hypotheses (alternative) : p < 0.095 (is corresponding to the claim)
The sample proportion is ,
p = 0.07
The test statistic is,
z = [tex]\frac{p - p_{0} }{\sqrt{\frac{p_{0}(1-p_{0}) }{n} } }[/tex]
z = [tex]\frac{0.07-0.095}{\sqrt{\frac{0.095(1-0.095)}{100} } }[/tex]
z = [tex]\frac{-0.025}{0.02932}[/tex]
z = -0.85
p value is 0.198
Critical value for this alpha level is - 1.96
Our test statistic value (-0.85) is greater than -1.96
Hence,
We fail to reject the null hypothesis.
Therefore,
The null hypothesis and the alternative hypothesis are opposite in content.
The alternative hypothesis usually need to be tested.
The alternative hypothesis is supported by rejecting the null hypothesis.
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