Question

Three separate random samples of students (one sample selected from each of three different colleges) were selected in order to estimate the population percentage of students at each college who are sophomores.

Sample 1: 120 students were selected from among all those attending college number 1 and 30 of them were found to be sophomores.

Sample 2: 65 students were selected from among all those attending college number 2 and 10 of them were found to be sophomores.

Sample 3: The sample from college number 3 showed that 30% of students were sophomores with a margin of error of (plus or minus) 10%.

(NOTE: You should only enter numbers in the blanks provided. For example, to enter "20%" you would type "20" in the blank.)

(b) If sample 2 is used to estimate the population percentage of students at college number 2 who are sophomores, what is the margin of error?
Enter margin of error as a percentage rounded to one decimal place:

Answer 1

ANSWER::

Sample 2:

n = Sample Size = 65

= Sample Proportion = 10/65 = 0.1538

SE= Sqrt(0.1538*(1-0.1538)/65

SE = 0.0447

Take = 0.05

From Table, critical values of Z = 1.96

So,

Marging of Error = 1.96 X 0.0447

= 0.0876

= 8.8%

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