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A hospital reported that the normal death rate for patients with extensive burns (more than $40%$ of skin area) has been significantly reduced by the use of new fluid plasma compresses. Pefore the new treatment, the mortality rate for extensive burn patients was about $60%$. Using the new compresses, the hospital found that only 49 of 85 pasients with extensive burns died. Use a $1%$ level of significance to test the claim that the mortality rate has dropped. (a) What are we testing in this problem? a single mean a difference of proportions a paired difference a single proportion a difference of means (b) What is the level of significance? State the null and alternate hypotheses. (Enter i for + as needed.) $H_{0}$
(c) What sampling distribution will you use? What assumptions are you making? We'll use the standard normal. We'll assume that a binomial experiment is an appropriate model for the probability distribution for the number of patients who die in a sample 85 patients with extensive burns and that the sample size is not too large so that we can use the normal approximation. We'll use the Student's $t$. We'll assume that a normal distribution is an appropriate model for the probability distribution for the number of patients who die in a sample 85 potients with extensive burns and that the sample size is not too large so that we can use the normal approximation. We'll use the student's $t$. We'll aswume that a normal distribution is an appropriate model for the probability distribution for the number of pabents who die in a sample 85 patients with extensive burns and that the sample size is sufficiently large so that we can use the normal approximation. We'll use the standard normal. We'll assume that a binomial experiment is an eppropriate model for the probability distribution for the mumber of patients who die in a sample 85 patients with extensive burns and that the sample size is sufficiently large so that we can use the normal approximation. What is the value of the standardized sample test statistic? (Round your answer to two decimal places.) (d) Find the P-value of the test statistic. (Round your answer to four decimal places.) P-value $=$ Sketch the sampling distribution and show the area corresponding to the P-value.

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