In 2013 the Harris Poll reported results of a survey about religious beliefs. Of 2252 American adults surveyed, 24% believed in reincarnation. Treating this as a random sample, a 95% confidence interval for the population proportion believing in reincarnation is (0.22, 0.26).

Without doing any new calculation, explain how the interval would change if the sample size had been only a fourth as large, n = 563.