# 8.1.2.1.2 - Example Handedness

8.1.2.1.2 - Example Handedness

Research Question: Are more than 80% of American's right handed?

In a sample of 100 Americans, 87 were right handed.

1. Check assumptions and write hypotheses

$np_0 = 100(0.80)=80$

$n(1-p_0) = 100 (1-0.80) = 20$

Both $np_0$ and $n(1-p_0)$ are at least 10 so we can use the normal approximation method.

This is a right-tailed test because we want to know if the proportion is greater than 0.80.

$H_{0}:p=0.80$
$H_{a}:p>0.80$

2. Calculate the test statistic
Test statistic: One Group Proportion

$z=\frac{\widehat{p}- p_0 }{\sqrt{\frac{p_0 (1- p_0)}{n}}}$

$\widehat{p}$ = sample proportion
$p_{0}$ = hypothesize population proportion
$n$ = sample size

$\widehat{p}=\frac{87}{100}=0.87$, $p_{0}=0.80$, $n=100$

$z= \frac{\widehat{p}- p_0 }{\sqrt{\frac{p_0 (1- p_0)}{n}}}= \frac{0.87-0.80}{\sqrt{\frac{0.80 (1-0.80)}{100}}}=1.75$

Our $z$ test statistic is 1.75.

3. Determine the p-value associated with the test statistic

This is a right-tailed 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 $p\; value=0.0401$.

4. Make a decision

$p\leq .05$, therefore our decision is to reject the null hypothesis

5. State a "real world" conclusion

Yes, there is statistical evidence to state that more than 80% of all Americans are right handed.

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