Question

what if we construct a confidence interval instead of a hypothesis test. in yhe dimple random sample of 331 americanadults who do not have a four year degree and are not currently enrollef in dchool 48% said tjey devidef not yo go to college because yhey could not afford school.

Answer 1

If we construct a confidence interval instead of a hypothesis test, we will get the same results for the two tailed test. In the given scenario, we are given the sample proportion as 0.48 or 48% and sample size as n = 331. If we find the confidence interval for the population proportion for the American adults who said they do not go to college because they could not afford school, then we will get two estimates such as lower limit and upper limit for this confidence interval for the population proportion. If the claimed proportion is lies between the lower and upper limit of confidence interval, then we do not reject the null hypothesis. If claimed proportion is not lies between the lower and upper limit of confidence interval, then we will reject the null hypothesis.

Note that results would be valid only in case of two tailed hypotheses tests. For the one tailed tests (either right tailed or left tailed), results will be vary; because confidence intervals in general only uses the two tailed critical values. One sided confidence intervals will provide the matching results with one sided tests.