Statistics

a. Null hypothesis, Ho: proportion of 2 day value is equal to control group mean. That is po = 0.9

Alternative Hypothesis, H1: proportion of 2 day value is greater than to control group mean. That is po > 0.9

Confidence interval for proportion = po ± (z(alpha)*sqrt((po*(1-po))/n)

Lower limit = 0.9 – (1.645*sqrt((0.9*0.1)/30)) = 0.80

Upper limit = 0.9 + (1.645*sqrt((0.9*0.1)/30)) = 0.99

Confidence interval = [0.80, 0.99]

Since my confidence interval includes 0.9, I may accept Ho and conclude that proportion of 2 day value is equal to control group mean. That is po = 0.9. 

Also, I am 95% confident that proportion of 2 day value lies in the interval [0.80, 0.99].

Here there is a possibility of Type II error which is accepting Ho when Alterative Hypothesis is true. I conclude that proportion of 2 day value is equal to control group mean. But however it is possible that proportion of 2 day value is greater than control group mean since the confidence interval also includes values greater than 0.9 which is [0.91, 0.99]