If you wish to estimate a population mean with a sampling error SE = .3 using a
ID: 3179653 • Letter: I
Question
If you wish to estimate a population mean with a sampling error SE = .3 using a 95% confidence interval and you know from prior sampling that sigma^2 is approximately equal to 7.2. how many observations would have to be included in your sample? Suppose you wish to estimate a population mean correct to within .20 with probability equal to .90. You do not know sigma^2, but you know that the observations will range in value between 30 and 34. a. Find the approximate sample size that will produce the desired accuracy of the estimate. You wish to be conservative to ensure that the sample size will be ample to achieve the desired accuracy of the estimate. b. Calculate the approximate sample size, malting the less conservative assumption that the range of the observation is equal to 6 sigma. In each case, find the approximate sample size required to construct a 95% confidence interval for p that has sampling error SE = .08. a. Assume p is near .2. b. Assume you have no prior knowledge about p, but you wish to be certain that your sample is large enough to achieve the specified accuracy for the estimate. The following is a 90% confidence interval for p: (.26, .54). How large was the sample used to construct this interval?Explanation / Answer
5.52) E=0.3
and for 95% CI, z=1.96
variance =7.2
hence sample size =varaince *(Z/E)2 ~ 308
5.64)here sample size =p(1-p)(z/E)2 =~97
for b) no prior information we will consider p=0.5
hence sample size =~151