Decreasing the sample size while holding the confidence level the same will do what to the width of your confidence interval?
A random sample of graduate students were asked, "Would you come back to school to get a second degree if you were given the opportunity?" Of the 150 people surveyed, 127 of them said that they would do so. Find a 95% confidence interval for the proportion of graduate students who would come back to school (Z_{a/2}Za/2​= 1.96). Round your answer to three decimal places.
The 99% confidence interval for a population proportion is [0.645, 0.737]. Find the standard error involved in this confidence interval. (Z_{a/2}Za/2​= 2.58).