A later poll on leaving
A referendum split 51.9% leave and 48.1% remain. A later sample of 500 people has 54% preferring to remain, so 46% preferring to leave. Test whether the leave proportion is still 0.519, against a two-sided alternative.
The standardised statistic is z=-2.64, and the two-sided standard-normal tail beyond 2.64 is about 0.0082. Also give an approximate 95% confidence interval for the leave proportion in the later poll.
Worked answer (click to show)
H_0:p=0.519 against H_1:p\neq 0.519. The observed leave proportion is 0.46. The statistic z=-2.64 has two-sided p-value about 0.0082, so the poll is not consistent with an unchanged leave proportion at level 0.05. An approximate 95% interval for the leave proportion is (0.42,\,0.50).