Question

An SRS of 55 lawyers from Reno, Nevada had a mean hourly salary of x= $310 and standard deviation s- $75 a. construct a 95% confidence interval for the mean hourly salary of all Reno lawyers b.find the margin of error in part a c. how large a sample would be necessary to have a margin of error of $25 with a 95% confidence level?

Answer 1

Solution:

n = 55

= 310

n = 55 bar{x} = 310 s = 75 (a) z = 1.96 95% confidence interval = 310 plusminus 1.96 (75/squareroot 55) = 310 plusminus 19.8214 = (290.1786, 329.8214) (b) margin of error = 1.96 (75/squareroot 55) = 19.8214 (c) ME = 25 we know that ME = z (s /squareroot n) 25 = 1.96 (75/squareroot n) squareroot n = 1.96*75/25 squareroot n = 5.88 n = 34.57 n almostequalto 35

s = 75

( a )

z = 1.96

95% confidence interval = 310 $\pm$ 1.96 (75/ $\sqrt{55}$ )

= 310 $\pm$ 19.8214

= ( 290.1786 , 329.8214 )

( b )

margin of error =  1.96 (75/ $\sqrt{55}$ )

= 19.8214

( c )

ME = 25

we know that

ME = z ( s / $\sqrt{n}$ )

25 = 1.96 ( 75 / $\sqrt{n}$ )

$\sqrt{n}$ = 1.96*75/25

$\sqrt{n}$ = 5.88

n = 34.57

n $\approx$ 35