Question

The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.6% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. What is the standard deviation ()? (Round your answer to four decimal places.)

a. 0.1762
b. 0.2459
c. 0.3138
d. 0.3914

Answer 1

The standard deviation of the sample can be calculated using the formula: = √( p(1-p) / n ). Given that 71.6% of the freshmen replied 'yes' in the survey, the standard deviation is approximately 0.1762.

Step-by-step explanation:

The standard deviation () of a sample can be calculated using the formula:

= √( p(1-p) / n )

Where:

• is the standard deviation
• p is the proportion of students who replied 'yes'
• n is the sample size

Given that 71.6% of the freshmen replied 'yes' in the survey, we can plug in the values to calculate the standard deviation.

= √( 0.716(1-0.716) / 8 )

≈ 0.1762

Therefore, the standard deviation is approximately 0.1762.