A confidence interval is desired for the true average stray-load loss µ (in watt

Question

A confidence interval is desired for the true average stray-load loss µ (in watts) for a certain type of induction motor when the line current is help at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with =3.0.

a) Compute a 95% CI for µ when n = 25 and ¯x = 61.2.

b) Compute a 95% CI for µ when n = 100 and ¯x = 61.2.

c) Compute a 80% CI for µ when n = 100 and ¯x = 61.2.

d) What is the smallest value of n for which the total width of the 90% CI does not exceed 1.0?

Explanation / Answer

a) z value at 95% = 1.96

s = 3 , n =25 , x = 61.2

CI = x + / - z * ( s/ sqrt(n))

= 61.2 + /- 1.96 *( 3 / sqrt(25))

= (60.024 , 62.376)

b)

z value at 95% = 1.96

s = 3 , n = 100 , x = 61.2

CI = x + / - z * ( s/ sqrt(n))

= 61.2 + /- 1.96 *( 3 / sqrt(100))

= (60.612 , 61.788)

c)

z value at 95% = 1.28

s = 3 , n =25 , x = 61.2

CI = x + / - z * ( s/ sqrt(n))

= 61.2 + /- 1.28 *( 3 / sqrt(25))

= (60.816 , 61.584)

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