Question

You plan to conduct a survey to find what proportion of METU students are satisfied with the social facilities of the university (rank at least 5). They will be asked to rate their university according to their perceptions regarding social facilities of the university from 1 to 10. You decide on the 99% confidence level and a margin of error of 3%. A pilot survey reveals that 8 of the 48 sampled students are satisfied with the social facilities of the university.

How many students should be interviewed to meet your requirements? (Round z-score to 3 decimal places. Round up your answer to the next whole number.)

Answer 1

Solution :

Given that,

= x / n = 8 / 48 = 0.17

1 - = 1 - 0.17 = 0.83

margin of error = E = 0.03

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.576 / 0.03)2 * 0.17 * 0.83

= 1040.34

sample size = n = 1041