Question

Suppose 20% of all heart transplant patients do not survive the operation. a. Think about taking repeated random samples of 251 patients from this population. Describe how the sample proportion who die would vary from sample to sample. (Hint: Be sure to refer to the shape, center, and spread of its sampling distribution.) Also include a well-labeled sketch to represent this distribution. b. Suppose you take a random sample of 251 heart transplant patients. Determine the probability that the sample proportion who die would be .213 or higher.

Answer 1

a) The 20% of all heart transplant patients do not survive the operation

that means p^ = 20 / 100

= 0.2

We have the sample of 251 patients.

means no of people would have die

n = 0.20 * 251

= 50.2 ~ 51

b) The probability that the sample proportion who die would be .213 or higher.

the samples are greater than 30

so we can use a Z test here to compute the probability,

Z = (p^ - p0) / {sqrt([p0(1-p0)]/n} ~ N ( 0, 1)

P[ p^ > 0.213 ] = P[ (p^ - p0) < (0.213 - 0.2) ]

= 1 - P[ (p^ - p0) < (0.213 - 0.2) ]

= 1 - P[ (p^ - p0) /{sqrt([p0(1-p0)]/n} < (0.213 - 0.2) / {sqrt([p0(1-p0)]/n} ]

= 1 - P ( Z < (0.213 - 0.2) / {sqrt([0.2 * (1-0.2)]/251}

= 1 - P ( Z < 0.013/0.02524778)

= 1 - P(Z < 0.5148968) ( From Z score table at 0.51 Z value at 0.05 level of significance)

= 1 - 0.7088

= 0.2912

So the probability that the sample proportion who die would be .213 or higher is 0.2912

>>>>>>>>>>>>>>>>> Best Luck >>>>>>>>>>>>>