Question

1. In addition to studying the mean tuition of this population of universities, the researcher wishes to study the proportion of universities in this population that regularly awards more than 50% of their student body some form of financial aid. What minimum numbers of universities are necessary to estimate the desired proportions under the following conditions? Explain the meanings of the minimum sample sizes you compute.

1. The estimate is desired to within ±15% with 98% confidence when the population proportion of universities that regularly awards financial aid to more than 50% of their student body is thought to equal 40%.

2. The estimate is desired to within ±15% with 98% confidence when the population proportion of universities that regularly awards financial aid to more than 50% of their student body is thought to be unknown.

3. The estimate is desired to within ±15% with 98% confidence when the population proportion of universities that regularly awards financial aid to more than 50% of their student body is thought to equal 70%.

Answer 1

SOLUTION A) 98% CONFIDENCE LEVEL , MARGIN OF ERROR= 0.15 and Proportion= 0.4

Z_(alpha/2) critical value for 98% confidence interval is 2.33

n=  Z^2_α/2 *p*(1-p) / MOE²,

n= (2.33)^2(0.4)*(1-0.4)/(0.15)^2

n= 5.4289*0.24*/0.0225

n= 57.9

n=58

The meaning of minimum sample size is sample required to test that if there is any variation is due to chance only.

b) When proportion is unknown we assume that the proportion is equal to 0.5

n= Z^2α/2 *p*(1-p) / MOE2

n= (2.33)^2*0.5*0.5/0.0225

n= 60.32

n=60

n= 60 is minimum sample required to test that if there is any variation is due to chance only.

c) Proportion= 0.7 (Given)

n= Z^2α/2 *p*(1-p) / MOE2

n= (2.33)^2*0.7*0.3/0.0225

n= 50.67

n=51

n= 51 is minimum sample required to test that if there is any variation is due to chance only.