Question

You take a random sample of 78 houses and find that 54 of them plan to give out chocolate  

A- Give the margin of error and the 95% confidence interval for the proportions of candies that are chocolate.

B- We want to still keep a 95% conference interval, but we want the interval to be narrower, what can be done? why does it work?

Answer 1

(A) = 54 / 78 = 0.6923

The Zcritical (2 tail) for = 0.05 is 1.96

The Confidence Interval is given by ME

The Lower Limit = 0.6923 - 0.1025 = 0.5898

The Upper Limit = 0.6923 + 0.1025 = 0.7948

The 95% Confidence Interval is (0.5898 , 0.7948)

(If required to 3 decimal, then the CI is 0.590, 0.795)

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(B) We know that

If we want to keep the level of confidence at 95%, then to decrease the width of the confidence interval, we need to increase the sample size.

This is because the sample size in the denominator, and therefore is inversely proportional to ME. That is as sample size increases, the ME decreases and vice versa. As ME decreases, the width also decreases.

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