In a trial of 167 patients who received 10-mg doses of a drug daily. 35 reported

Question

In a trial of 167 patients who received 10-mg doses of a drug daily. 35 reported headache as a side effect. Use this information to complete parts (a) through (d) below: Obtain a point estimate for the population proportion of patients who received 10-mg doses of a drug daily and reported headache as a side effect. p = (Round to two decimal places as needed) Verify that the requirements for constructing a confidence interval about p are satisfied. Are the requirements for constructing a confidence satisfied? Yes, the requirements for constructing a confidence interval are satisfied. No, the requirements that each trial be independent is not satisfied. No, the requirement that np(1 - p) is greater than 10 is not satisfied. No, the requirement that the sample size is no more than 5% of the population is not satisfied. Construct a 95% confidence interval. Which statement below best interprets the interval? We are 95% confident that the interval contains the true value of p. There is a 95% chance that the true value of p will not fall in the interval. We are 95% confident that the interval does not contain the true value of p. There is a 95% chance that the true value of p will fall in the interval.

Explanation / Answer

a)
Note that              
              
p^ = point estimate of the population proportion = x / n = 35/167 =    0.209580838   [ANSWER]

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b)

All requirements indicated in options B to D are all actually satisfied. Hence,

OPTION A: Yes the requirements for constructing a confidence interval are satisfied.   [ANSWER]

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c)     
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.031495339          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.061729729          
lower bound = p^ - z(alpha/2) * sp =   0.147851109          
upper bound = p^ + z(alpha/2) * sp =    0.271310568          
              
Thus, the confidence interval is              
              
(   0.147851109   ,   0.271310568   ) [ANSWER]

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d)

OPTION D: The is a 95% chance that the true value of p will fall in the interval. [CONCLUSION]

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