Question

when the level of confidence and sample proportion remain the same, a confidence interval for a population proportion based on a sample of n=200 will be narrower than a confidence interval based in a sample of n=100. True or False

Answer 1

margin of error which is Confidence interne for population proportion is calculated using the formulazz= Jē (1-6), where Da sample proportion Zo = Cortical value and it depends on the confidence level and n = Sample size. Width of the interval is determined by the 2 * 80,- As n is in the denominator ; as the value of n increases (keeping the Confidence level and the sample proportion unchanged the value of margin of erroy decreases. When the margin of error decrease the width of the interval decreases as well; and this will make the confidence interval narrower. Therefore confidence interval for population proportion based on on a sample of 1-200 will be narrower than a confidence interal based on sample q n=100 ; When the level of constidence and sample popportion remain the same. Hence Answer is : TRUE