Question

In: Statistics and Probability

In a clinical trial, 159 flu patients took a newly developed drug and 103 of them...

In a clinical trial, 159 flu patients took a newly developed drug and 103 of them recovered from the flu within 48 hours.

a. What is the sample statistic (p̂ or ȳ)? Please calculate/write its value.

b. Construct a 95% confidence interval for the true proportion of all flu patients who will recover within 48 hours of taking this new drug. Provide the interval in (left endpoint, right endpoint) format.

c. Interpret the meaning of your confidence interval in the context of the study.

d. Based on your confidence interval, is a 75% rate of recovery plausible? Why or why not?

Expert Solution

Number of patients who took a newly developed drug : n=159

Number of patients of 159 who recovered from the flu : x = 103

a.

a. What is the sample statistic (p̂ or ȳ)? Please calculate/write its value.

The sample statistic is sample proportion :

sample proportion : = x/n = 103/159 = 0.6478

b. Construct a 95% confidence interval for the true proportion of all flu patients who will recover within 48 hours of taking this new drug.

Confidence interval for true (population) Proportion:p

for 95% confidence level = (100-95)/100 =0.05

/2 =0.05/2 =0.025;

Z/2 = Z0.025 = 1.96

95% confidence interval for the true proportion of all flu patients who will recover within 48 hours of taking this new drug.

95% confidence interval for the true proportion of all flu patients who will recover within 48 hours of taking this new drug = (0.573554,0.722046)

c. Interpret the meaning of your confidence interval in the context of the study.

With 95% confidence it can be said that proportion of all flu patients who will recover within 48 hours of taking this new drug is between 0.573554 and 0.722046

d.. Based on your confidence interval, is a 75% rate of recovery plausible? Why or why not?

As 0.75 as outside the 95% confidence interval (0.75 is less than 0.722046 : right end point upper confidence limit ) , 75% rate of recovery is not plausible.

orchestra answered 2 years ago

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