Question

The one-sample z-test for proportions determines the p-value using the “normal approximationmethod”. (Note that in class we talked about the two-sample z-test for proportions, but the ideas are similar for the one sample case). This method approximates the exact p-value that would have been found if the binomial formula were used. But, the “normal approximation method” only works well when the sample size is “large enough”. Write a paragraph that discusses the following: Why is the one-sample z-test for proportions used instead of just using the binomial formula to find p-values? Do you think it is necessary to use the one-sample z-test for proportions for “large sample sizes” with the advent of technology? Explain.

Answer 1

It is necessary to use the one-sample z-test for proportions for “large sample sizes” with the advent of technology due to the above advantages over binomial test as it is not just for easy calculation that we use z- test but for several other reasons and we also take care to see if the sample is sufficiently large to be eligible for z- test and normal approximation to the binomial is used and we make continuity correction to make it closer to binomial distribution.