8.1.2.1.2  Example: Handedness
8.1.2.1.2  Example: HandednessResearch Question: Are more than 80% of American's right handed?
In a sample of 100 Americans, 87 were right handed.
\(np_0 = 100(0.80)=80\)
\(n(1p_0) = 100 (10.80) = 20\)
Both \(np_0\) and \(n(1p_0)\) are at least 10 so we can use the normal approximation method.
This is a righttailed test because we want to know if the proportion is greater than 0.80.
\(H_{0}\colon p=0.80\)
\(H_{a}\colon p>0.80\)
 Test statistic: One Group Proportion

\(z=\dfrac{\widehat{p} p_0 }{\sqrt{\frac{p_0 (1 p_0)}{n}}}\)
\(\widehat{p}\) = sample proportion
\(p_{0}\) = hypothesize population proportion
\(n\) = sample size
\(\widehat{p}=\dfrac{87}{100}=0.87\), \(p_{0}=0.80\), \(n=100\)
\(z= \dfrac{\widehat{p} p_0 }{\sqrt{\frac{p_0 (1 p_0)}{n}}}= \dfrac{0.870.80}{\sqrt{\frac{0.80 (10.80)}{100}}}=1.75\)
Our \(z\) test statistic is 1.75.
This is a righttailed test so we need to find the area to the right of the test statistic, \(z=1.75\), on the z distribution.
Using Minitab Express, we find the probability \(P(z\geq1.75)=0.0400592\) which may be rounded to \(p\; value=0.0401\).
\(p\leq .05\), therefore our decision is to reject the null hypothesis
Yes, there is statistical evidence to state that more than 80% of all Americans are right handed.