Data a discusses a study designed to test whether applying a metal tag is detrimental to a penguin, as opposed to applying an electronic tag. One variable examined is the date penguins arrive at the breeding site, with later arrivals hurting breeding success. Arrival date is measured as the number of days after November 1st. Mean arrival date for the 167 times metal-tagged penguins arrived was December 7th (37 days after November 1st) with a standard deviation of 38.77 days, while mean arrival date for the 189 times electronic-tagged penguins arrived at the breeding site was November 21st (21 days after November 1st) with a standard deviation of 27.50. Do these data provide evidence that metal-tagged penguins have a later mean arrival time?
(a) State the null and alternative hypothesis
(b) Give test statistic and p-value
(c) Do these data provide evidence that metal tagged penguins have a later mean arrival time, yes or no?