Question

3. + -19 points DevoreStat9 7.E.004. My Notes + Ask Your Teacher A CI is desired for the true average stray-load loss u (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with 2.0. (Round your answers to two decimal places.) (a) Compute a 95% CI for u when n = 25 and x = 51.1. watts (b) Compute a 95% CI for u when n = 100 and x = 51.1. watts (c) Compute a 99% CI for u when n = 100 and x = 51.1. watts 51.1. (d) Compute an 82% CI for when n = 100 and X ( watts (e) How large must n be if the width of the 99% interval for p is to be 1.07 (Round your answer up to the nearest whole number.) n = You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help?

Answer 1

Part a)
Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )
Critical value Z(α/2) = Z (0.05 /2) = 1.96 (From Z table)
51.1 ± Z (0.05/2 ) * 2/√(25)
Lower Limit = 51.1 - Z(0.05/2) 2/√(25)
Lower Limit = 50.32
Upper Limit = 51.1 + Z(0.05/2) 2/√(25)
Upper Limit = 51.88
95% Confidence interval is ( 50.32 , 51.88 )

Part b)
Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )
Critical value Z(α/2) = Z (0.05 /2) = 1.96  (From Z table)
51.1 ± Z (0.05/2 ) * 2/√(100)
Lower Limit = 51.1 - Z(0.05/2) 2/√(100)
Lower Limit = 50.71
Upper Limit = 51.1 + Z(0.05/2) 2/√(100)
Upper Limit = 51.49
95% Confidence interval is ( 50.71 , 51.49 )

Part c)
Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )  
Critical value Z(α/2) = Z (0.01 /2) = 2.576  (From Z table)
51.1 ± Z (0.01/2 ) * 2/√(100)
Lower Limit = 51.1 - Z(0.01/2) 2/√(100)
Lower Limit = 50.58
Upper Limit = 51.1 + Z(0.01/2) 2/√(100)
Upper Limit = 51.62
99% Confidence interval is ( 50.58 , 51.62 )

Part d)
Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )
Critical value Z(α/2) = Z (0.18 /2) = 1.341  (From Z table)
51.1 ± Z (0.18/2 ) * 2/√(100)
Lower Limit = 51.1 - Z(0.18/2) 2/√(100)
Lower Limit = 50.83
Upper Limit = 51.1 + Z(0.18/2) 2/√(100)
Upper Limit = 51.37
82% Confidence interval is ( 50.83 , 51.37 )

Part e)
Sample size can be calculated by below formula
n = ( 2 * Z(α/2) * σ / W )²
n = (2 * Z(0.01/2) * (2 / 1) )²
Critical value Z(α/2) = Z(α/2) = 2.5758
n = (( 2 * 2.5758 * (2 / 1 ) )²
n = 107
Required sample size at 99% confident is 107