Question

Various studies indicate that approximately 9% of the world's population is left handed. You think this number is actually higher. You take an SRS of 222 people and find that 23 of them are left handed. Test your claim at the 5% significance level.

1. State your null and alternative hypotheses.

2.State the rejection region.

3. Calculate the test statistic.

4.Determine the P-value for your test.

5. State your conclusion for your hypothesis test.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.09
Alternative Hypothesis, Ha: p > 0.09

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1036 - 0.09)/sqrt(0.09*(1-0.09)/222)
z = 0.71

P-value Approach
P-value = 0.2389
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the proportion is greater than 9%