2. Metal Tags on Penguins and Survival. 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 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. Test whether the survival rate is lower among meta tagged penguins than among electronic-tagged penguins. Use subscripts E for Electronic and M for Meta a. State hypotheses. Ho PE = PM Ha: P₂Pm b. Calculate the sample statistic PE - PM 18 10 8 PE - Pm = = 0.14 50 2= 50 c. Use Normal distribution methods to calculate a z-test statistic, given SE = 0.0898. PE - PM SE 1.7817 = -1 0.16 0.0898 d. Find the p-value and draw a Normal curve with z-statistic and appropriate shaded region. P-valve 0.0374 0.0314 Normal curve: LI Z 3 shaded region 1.7817 to 00 e. State the conclusion of the test in context, using nontechnical language. 0.16 1 1.7817 g. Interpret the confidence interval. (in excel) p-value: P- værver =) ~ (NORM. DIST (1.7817,91, TRUE) = J f. Find a 90% confidence interval to three decimal places for this difference in proportions, given SE = 0.08836. Show your calculations.

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