Answer:
0.0721
Step-by-step explanation:
A 95% confidence interval for the population proportion is calculated using the formula;
[tex]p+/-1.96\sqrt{\frac{p(1-p)}{n} }[/tex]
In this case p is the sample proportion, calculated as ;
number of successes/sample size. It is the equivalent of the probability of success in a binomial distribution. This implies that the sample proportion in this case will be; 97/184
The value 1.96 is the confidence coefficient associated with a 95% confidence interval for the population proportion since the sample proportions under the central limit theorem are assumed o be normally distributed.
n is simply the sample size, 184 college students.
Now, the expression
[tex]1.96\sqrt{\frac{p(1-p)}{n} }[/tex] is what is termed as the margin of error for a 95% confidence interval of the population proportion. We simply substitute the values given into the expression and simplify it.
[tex]1.96\sqrt{\frac{\frac{97}{184} (1-\frac{97}{184} )}{184} }\\ =0.0721[/tex]
