Standard Error of the Sample Proportion Sampling Distributio

Standard Error of the Sample Proportion Sampling Distribution (SEP) = estimated standard deviation of the sample proportion sampling distribution = V(sample proportion*(1-sample proportion)/sample size) 1. A random sample of 100 freshmen students at University Park campus is taken to estimate the percentage of freshmen that have taken a tour of Pattee Library during orientation week. Of the 100 freshmen, 40 (40%) of them have taken a tour of Pattee Library. The standard error (SE) for a sample percentage in this situation is estimated to be approximately. A) 4.0% B) 4.9% C) 0.24% D) 24% 2. A random sample of 400 freshmen students at University Park campus is taken to estimate the percentage of freshmen who have taken a tour of Pattee Library during orientation week. Of the 400 freshmen, 160 (40%) of them have taken a tour of Pattee Library. The standard error (SE) for a sample percentage in this situation is estimated to be approximately. A) 4.9% B) 4.0% C) 2.45% D) 24% 3. When the sample size increases by 4 times (going from a sample of size 100 to a sample of size 400 with everything else remaining the same), the SE of the sampling distribution for our sample proportion is: A) 1/2 as large as it was before the sample size increase 8) 2 times larger than it was before the sample size increase C) 4 times larger than it was before the sample size increase D) 1 as large as it was before the sample size increase

Solution

1) standard error =sqrt( 0.4 * 0.6 / (100) )= 0.049....option(B)
2) std. error = sqrt( .4 * .6 / (400 ) )= 0.0245.....option(c)
3) (A) 1/2 times large...