A physician with a practice is currently serving 290 patient

A physician with a practice is currently serving 290 patients. The physician would like to administer a survey to his patients to measure their satisfaction level with his practice. A random sample of 22 patients had an average satisfaction score of 7.7 on a scale of 1-10. The sample standard deviation was 1.6. Complete parts a and b below.

a. 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 ( , )

b. What assumption needs to be made for this analysis?

A.

The population is normally distributed.

B.

The population standard deviation is known.

C.

The sample size is less than 5% of the population.

D.

There are no assumptions needed for this analysis.

Solution

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 =    7.7          
t(alpha/2) = critical t for the confidence interval =    2.831359558          
s = sample standard deviation =    1.6          
n = sample size =    22          
df = n - 1 =    21          
Thus,              
              
Lower bound =    6.734163382          
Upper bound =    8.665836618          
              
Thus, the confidence interval is              
              
(   6.734163382   ,   8.665836618   ) [ANSWER]

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B)

OPTION A:

A. The population is normally distributed. [ANSWER]