Im on a online program and this teacher doesnt fully explain

Im on a online program and this teacher doesn\'t fully explain how to do these kind of problems.. please help and explain how to do these?

A random sample of 5000 people was chosen for a survey. 38% of them had dogs. Find the 95% confidence interval.

it has an equation like this \" o= sqrt( p(1-p)/n )

Thanks for reading!

Solution

38% of the people had dogs. Hence p (probability) is equal to 0.38

The 95% confidence interval is defined as the range of values such that the probability that the actual result is within that range is 95%.

For obtaining the confidence interval, standard deviation of the data has to be calculated first.

Standard deviation = [sqrt((p(1-p))/n)] [= sqrt(((0.38)(0.62))/5000) ]

[= 0.0068644 ~~ 0.686%]

The z-value for 95% (two tailed test) is 1.96 standard deviations.

So the 95% confidence interval is [38% +- 1.96*0.686] , or about
39.3% to 36.7%

The spread is therefore, 2.6%.