A physician with a practice is currently serving 300 patients. The physician wou
ID: 3441946 • Letter: A
Question
A physician with a practice is currently serving 300 patients. The physician would like to administer a survey to his patients to measure their satisfaction level with his practice. A random sample of 25 patients had an average satisfaction score of 7.6 on a scale of 1-10. The sample standard deviation was 1.5. Complete parts a and b below. Construct a 99% confidence interval to estimate the average satisfaction score for the physician's practice. The 99% confidence interval to estimate the average satisfaction score is ( , ). (Round to two decimal places as needed.) What assumption needs to be made for this analysis? The population standard deviation is known. The population is normally distributed. The sample size is less than 5% of the population. There are no assumptions needed for this analysis.Explanation / Answer
A)
Note that
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 7.6
t(alpha/2) = critical t for the confidence interval = 2.796939505
s = sample standard deviation = 1.5
n = sample size = 25
df = n - 1 = 24
Thus,
Lower bound = 6.760918149
Upper bound = 8.439081851
Thus, the confidence interval is
( 6.760918149 , 8.439081851 ) [ANSWER]
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B)
OPTION B. The population is normally distributed. [ANSWER, OPTION B]
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