In Exercise 6.178 on page 403 we perform a test 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, 33 of the 167 metal-tagged penguins survived while 68 of the 189 electronic-tagged penguins survived.

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

(b) State the null and alternative hypotheses.

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

(d) Calculate the chi-square test statistic.

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

Exercise 6.178

Data 1.3 on page 10 discusses a study designed to test whether applying metal tags is detrimental to penguins. One variable examined is the survival rate 10 years after tagging. The scientists observed that 10 of the 50 metal tagged penguins survived, compared to 18 of the 50 electronic tagged penguins. Construct a 90% confidence interval for the difference in proportion surviving between the metal and electronic tagged penguins (p_M − p_E). Interpret the result.