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?

Answers

Answer 1

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

Step-by-step explanation:

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

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

For 95% confidence level , z* = 1.96

As, [tex]\sigma[/tex] = 8.265, E = 1

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

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


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Step-by-step explanation:

[tex]if \: the \: numbers \: of \: shirts \: is \: s.\\ if \: the \: numbers \: of pants \: is \: p. \\then \: the \: inequality \: that \: represents \: \\ the \: numbers \: of \: shirts \: and \: pants \: you \: can \: afford \: is : \\ 9.5s \: + \: 16p \: = 24.[/tex]

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Step-by-step explanation:

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