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3241004551 [841]
3 years ago
5

Sarah is doing research on the average age of first-year resident physicians. She wants her estimate to be accurate to within 1

year. From past studies, she knows the population standard deviation is 8.265. How many first-year residents must she survey to be 95% confident?
Mathematics
1 answer:
WINSTONCH [101]3 years ago
7 0

Answer: The number of first-year residents she must survey to be 95% confident= 263

Step-by-step explanation:

When population standard deviation (\sigma)  is known and margin of error(E) is given, then the minimum sample size (n) is given by :-

n=(\dfrac{z^*\sigma}{E})^2, z* = Two-tailed critical value for the given confidence interval.

For 95% confidence level , z* = 1.96

As, \sigma = 8.265, E = 1

So, n= (\dfrac{1.96\times8.265}{1})^2 =(16.1994)^2\\\\= 262.42056036\approx263\ \ \ [\text{Rounded to the next integer}]

Hence, the number of first-year residents she must survey to be 95% confident= 263

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