Answer: 95% confidence interval for the proportion of yellow is (0.125,0.275).
Step-by-step explanation:
Since we have given that
n = 22+22+22+12+15+15=108
x = yellow = 22
So, [tex]\hat{p}=\dfrac{22}{108}=0.20[/tex]
We need to find the 95% confidence interval.
So, z = 1.96
So, Interval would be
[tex]\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.20\pm 1.96\times \sqrt{\dfrac{0.2\times 0.8}{108}}\\\\=0.20\pm 0.075\\\\=(0.20-0.075, 0.20+0.075)\\\\=(0.125, 0.275)[/tex]
Hence, 95% confidence interval for the proportion of yellow is (0.125,0.275).
