Question

A test is performed for the difference in the proportion of penguins who survive over a 10-year period, between penguins tagged with metal tags and those tagged with electronic tags. We are interested in testing whether the type of tag has an effect on penguin survival rate, this time using a chi-square test. The results from the study are in the table below.

	Metal	Electronic	Total
Survived	37	64	101
Died	123	119	242
Total	160	183	343

At a 5% significance level, perform a χ 2 test to test the claim:

Ho: Survival status is not associated with the type of tag.

Ha: Survival status is associated with the type of tag.

a) Write the expected values for the four cells in the table. Round to one decimal place.

Metal and survived:

Metal and died:

Electronic and survived:

Electronic and died:

b) Write the ?² contribution for each of the four cells. Round to two decimal places.

Metal and survived:

Metal and died:

Electronic and survived:

Electronic and died:

c) Find the ?²-test statistic. Show your work. Round to two decimal places.

d) What are the degrees of freedom?

e) Use your ?²-test statistic to find the p-value on a ?²-distribution. Round your p-value to three decimal places.

f) State your conclusion in context.

Answer 1