Answer:
Explanation:
in the first part have to assume that nothing is known and want a 90% confidence interval. We want a 90% confidence interval and in the first part we want to assume that nothing is known. So what is the formula in this case? And is equal to Z Alfa by two square in 20 point to fight upon E square. Okay, what is going to be Alfa by two? Alfa by two will be 0.5 Since my Alfa is 0.1 my alphabet 0.5 So what is going to be the value off Z Alfa? By two it is going to be 1.645 So my Z Alfa by two in both the calculations will be 1.64 fight one point export fight. Okay, now what will be the value off either? I put I will put my e equal to 0.0 to my evil. Be 0.2 in this case, right? Okay, because I want my sample percentage. You know, I want to be 19% confident that the sample percentages within 2% points off the 2% for the population off all adults. So I have all the values. And if I put them over here, I will get the value for my end. Okay, I will get the value for N to be equal to 1692 1692 This is my required sample size. Moving on to part B. What will be Parke B in part B? They're saying that 95% of what else have had chicken pox. Okay, 95% of the areas have had chickenpox. So my peak cap is going to be 950.95 Peak up is going to be 0.95 And therefore, what will be my cue cap? My cue cap will become 0.5 Okay, Now, in this case, I want to find n and the formula for that is their alphabet, which is going to be the same 1.645 square into now. Because I know P Cap, the formula is going to be instead of 0.25 Now we have P cap, you cap upon e square again. Everything else is same. We have just added these two values P cap, you cap the value of whose we know the value of whom we know. 0.950 point 05 So my end in this case turns out to be 3. 22 3, 22. Okay, this is the required sample sizes. So does the added knowledge and part. We have much effect on the sample size. Well, I would say definitely, but we're here. It was around five times. Okay, so the sample size is reduced around five times away in part B.