Question

Metal Tags on Penguins

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. In the study, 34 of the 154 metal-tagged penguins survived while 61 of the 177 electronic-tagged penguins survived.

(a) Create a two-way table from the information given.

	Metal	Electronic	Total
Survived	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement
Died	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement
Total	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement	Enter your answer in accordance to item (a) of the question statement

(b) Give a table with the expected counts for each of the four categories.

Round your answers to two decimal places.

	Metal	Electronic
Survived	Enter your answer in accordance to item (b) of the question statement	Enter your answer in accordance to item (b) of the question statement
Died	Enter your answer in accordance to item (b) of the question statement	Enter your answer in accordance to item (b) of the question statement

(c) Calculate the chi-square test statistic.

Round your answer to one decimal place.

chi-square statistic = Enter your answer in accordance to item (c) of the question statement

(d) Determine the p-value and state the conclusion.

Round your answer to three decimal places.

p-value = Enter your answer in accordance to item (d) of the question statement


Conclusion: Choose the answer from the menu in accordance to item (d) of the question statement                                                          RejectDo not reject H0.

Is survival rate related to the type of tag?

Choose the answer from the menu in accordance to item (d) of the question statement                                                          YesNo

Answer 1

a)

Oi	Metal	Electronic	Total
survived	34	61	95
Died	120	116	236
total	154	177	331

b)

Ei=row total*column total/grand total	Metal	Electronic
survived	44.20	50.80
Died	109.80	126.20

c)

applying chi square test:

chi square    χ2	=(Oi-Ei)2/Ei	Metal	Electronic	Total
	survived	2.3536	2.0478	4.401
	Died	0.9474	0.8243	1.772
	total	3.301	2.872	6.173

chi-square test statistic =6.2

d)

p value =0.013

reject Ho , if level of significance is greater than 0.013