Question

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. Before the new treatment, the mortality rate for extensive burn patients was about 60%. Using the new compresses, the hospital found that only 41 of 88 patients with extensive burns died. Use a 1% level of significance to test the claim that the mortality rate has dropped

a) What is the value of the standardized test statistic? (Round your answer to two decimal places.)

b) Find the P-value. (Round your answer to four decimal places.)

Answer 1

H0: p = 0.60

Ha: p < 0.60 (Left tailed)

Sample proportion $\hat{p}$ = 41 / 88 = 0.4659

a)

Test statistics

z = $\hat{p}$ - p / sqrt ( p ( 1 - p) / n)

= 0.4659 - 0.60 / sqrt( 0.60 * 0.40 / 88)

= -2.57

b)

p-value = P( Z < z)

= P( Z < -2.57)

= 1 - P( Z < 2.57)

= 1 - 0.9949

p-value = 0.0051

Since p-value < 0.01 level , reject the null hypothesis and support the claim.