When to Use What: For each example below you would start to construct a confiden

Question

When to Use What: For each example below you would start to construct a confidence interval by identifying which distribution should be used to find the margin of error. It is possible that you won't be able to use either distribution.

(a) a confidence interval for a population proportion where n = 65 and there are 3 successes in your sample leading to a sample proportion of 0.046

z-distribution

t-distribution    

neither distribution

(b) a confidence interval for a population proportion where n = 69 and there are 59 successes in your sample leading to a sample proportion of 0.855

z-distribution

t-distribution    

neither distribution

Explanation / Answer

a) Since np = 2.99<5, we can use netiher distribution

b) Since np = 58.995>5, we use z distribution for population proportion

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