5 6 A random sample of 144 patients suffering from a partic

5 - 6. A random sample of 144 patients, suffering from a particular disease are given a new medicine, 108 of the patients report an improvement in their condition. 6. d) Construct a 90% confidence lower bound for the overall improvement rate. e) Construct a 95% confidence upper bound for the overall improvement rate. f) The company that manufactures this medicine claims an 80% improvement rate. Based on your answer to part (e), do you find this claim believable? Explain your answer.

Solution

d).

P =108/144=0.75

Z value for 90% = 1.645

CI = p \\pm z* \\sqrt {(p*(1-p)/(n))}

CI = 0.75 \\pm 1.645* \\sqrt{(0.75*(1-0.75)/(144))}

=( 0.6906, 0.8094)

90%   lower bound = 0.6906

e).

P =108/144=0.75

Z value for 95% = 1.96

CI = p \\pm z* \\sqrt {(p*(1-p)/(n))}

CI = 0.75 \\pm 1.96* \\sqrt{(0.75*(1-0.75)/(144))}

95% =( 0.6793, 0.8207)

95%   upper bound = 0.8207

f).

we can believe the 80% improvement rate because ( 80%) , 0.8 in falls below the 95% upper Confidence interval.