Hello I have solved this question but I am not sure if the hypothesis test should look like this. Could you look ar my solution and inform me wheher or not I answered this question correctly? Would be very grateful!

Question: Suppose you want to estimate the proportion (?) of population that had covid. To do so, you survey a random sample of people. Your survey from 20 people shows the following answers: N,N,N,N,Y, N,N,N,N,N, N,N,N,Y,N, Y,N,N,N,N, where Y- yes (had covid), N-no (did not have covid).Given your prior and all the evidence, find 90% equal-tailed Bayesian credible interval for ?. Test the hypothesis that for every 100 people, the number of people who had covid is fewer than or equal to 30 people (H0- null) at 10 % significance level.

Solution in the photo:

H: . 5 0 3 1 My : 1. 7 0 3 (*// tailed test ) a = al ascore = 1, 28 Prior bela ( 6, 14 ) n= 20 4= 3 Posterior ~beta ( 9; 31) Posterior mean = 0, 225 Posterior sd = 0,0 42 CT: 0 225 + 1, 28 . 0,042 => LO, 17 0, 281 Answer: 0, 3, does not belong to OCI hence REJECT Ho