Question

6.222 Metal Tags on Penguins and Length of Foraging Trips Data were collected over a 10-year timespan from a sample of 100 penguins that were randomly given either metal or electronic tags. One variable examined is the length of foraging trips. Longer foraging trips can jeopardize both breeding success and survival of chicks waiting for food. Mean length of 344 foraging trips was 12.70 days for metal-tagged penguins. Mean length of 512 foraging trips was 11.60 days for electronic-tagged penguins. An estimate of the standard error for this difference of means is SE=0.283.

a. We will address the question of whether foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins. State hypotheses in terms of two means.

b. Calculate the sample statistic xM - xE

c. Calculate a t-test statistic, using the given estimate of SE.

d. What are the correct (conservative) degrees of freedom for a t-distribution for this test?

e. Use t-distribution methods to find the p-value and draw a rough curve with appropriate shaded region. You may give either a precise p-value from software or bounds on a p-value from Table A.

f. State the conclusion of the test in context, using nontechnical language.

Answer 1

a) NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

b) The sample statistic xM-xE= 12.70-11.60= 1.10 days.

c) t test = xM-xE/S.E = 1.10/0.283= 3.89

d) Min(n1-1,n2-1)= min(344-1,512-1)= min(343,511)= 343 d.f

e) P value = 6.02029E-05= 0.0000602029

P value <0.05 level of significance. Hence significant.

Decision: Reject null hypothesis H0

f) We have enough evidence to conclude that foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins.